All practice questions

Question 6581Question →

A chemist is given a dry solid mixture containing nickel powder, ammonium chloride ( $NH_4Cl$ ), fine barium sulfate ( $BaSO_4$ ) powder, and sodium chloride ( $NaCl$ ). What is the correct chronological sequence of laboratory procedures required to isolate each pure component from the mixture?

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence of separation steps is: 1. Pass a magnet over the dry solid mixture to isolate nickel powder. 2. Heat the dry residue to sublime ammonium chloride. 3. Add distilled water to dissolve sodium chloride. 4. Centrifuge the suspension to spin down fine barium sulfate powder. 5. Decant the clear supernatant liquid and evaporate to dryness to recover sodium chloride crystals.

The correct sequence begins with magnetization on the dry solid mixture to remove ferromagnetic nickel. Next, sublimation is performed on the dry residue to separate ammonium chloride, which must occur before adding water because both ammonium chloride and sodium chloride are water-soluble. Distilled water is then added to selectively dissolve sodium chloride while leaving barium sulfate in suspension. Centrifugation rapidly spins down the fine barium sulfate precipitate. Finally, decanting and evaporating the clear supernatant liquid yields pure sodium chloride crystals.

Step-by-Step Solution

1

Extract ferromagnetic nickel powder using a bar magnet.

Dry nickel powder is separated cleanly from the solid mixture.

Nickel is ferromagnetic and is attracted by a magnetic field without requiring chemical reagents or solvent addition.

2

Apply controlled heat to the dry residue under an inverted funnel to sublime ammonium chloride (

NH_4Cl

).

Ammonium chloride sublimates directly into gas upon heating and deposits as pure solid crystals on the cool funnel surface.

Sublimation must precede water dissolution because both

NH_4Cl

and

NaCl

are soluble in water; dissolving first would make thermal separation of the two salts impossible.

3

Add distilled water to the remaining mixture of

NaCl

and

BaSO_4

and stir.

Sodium chloride dissolves into aqueous solution (

NaCl_{(aq)}

) while insoluble

BaSO_4

forms a fine suspension.

Water acts as a selective solvent based on solubility differences between soluble

NaCl

and insoluble

BaSO_4

.

4

Spin the suspension in a laboratory centrifuge.

Dense, fine particles of

BaSO_4

compact tightly at the bottom of the tube, separating clearly from the aqueous liquid.

Centrifugation rapidly forces fine suspended solids out of liquid phase much faster and more completely than gravity filtration.

5

Decant the supernatant solution and evaporate the solvent.

Water evaporates off, yielding pure crystalline sodium chloride.

Evaporation separates a non-volatile soluble solid solute from its volatile liquid solvent.

Key Concept

Sequential Separation of Multi-Component Mixtures

Question 6582Question →

Read the dramatic excerpt below:

EZE: (Addressing the assembled elders in the palace yard)
Thirty years ago, our forefathers pledged this sacred grove to the spirit of the hills. Today, the strangers arrive with machines to fell the ancient trees, unaware of the curse that awaits any who disturb the soil.

In the structural development of a play, Eze's speech in this scene functions primarily as

exposition, by providing essential background history and introducing the underlying conflict

the climax, by bringing the central confrontation to its peak emotional resolution

dramatic irony, because the characters on stage hold secret knowledge that the audience lacks

a soliloquy, by portraying an isolated character reflecting privately on his tragic flaw

Show answer & explanation

Answer: exposition, by providing essential background history and introducing the underlying conflict

Answer

The correct answer is the option identifying the speech as exposition, by providing essential background history and introducing the underlying conflict.

The passage serves as exposition because Eze informs both the onstage elders and the audience about critical past events (the pledge made thirty years ago) and the impending crisis (the arrival of strangers with logging machines). This establishes the context, setting, and foundational conflict of the drama.

Step-by-Step Solution

1

Analyze the dramatic context and audience of the speaker

Eze speaks publicly to assembled elders about historical events ('Thirty years ago') and an impending crisis ('Today, the strangers arrive').

Identifying who is present and what information is conveyed determines whether the speech is a public address, soliloquy, or structural device.

2

Determine the structural function of the speech within plot development

The speech introduces past events and sets the stage for the primary conflict between sacred tradition and modern intrusion.

Background information that sets up the story's initial conditions and conflict constitutes exposition.

Key Concept

Dramatic Exposition and Structural Plot Elements

Question 6583Question →

A container holds an unknown gas, $Y$ . It takes $15\text{ seconds}$ for a specific volume of gas $Y$ to effuse through a fine orifice. Under identical temperature and pressure conditions, the same volume of oxygen gas ( $O_2$ ) requires $30\text{ seconds}$ to effuse through the same orifice. What is the molar mass of gas $Y$ ? [Molar mass of $O_2 = 32\text{ g/mol}$ ]

8\text{ g/mol}

16\text{ g/mol}

64\text{ g/mol}

128\text{ g/mol}

Show answer & explanation

Answer: $8\text{ g/mol}$

Answer

The molar mass of gas

Y

is

8\text{ g/mol}

.

By Graham's Law of Effusion, the time required for equal volumes of two gases to effuse under identical conditions is directly proportional to the square root of their molar masses:

\frac{t_1}{t_2} = \sqrt{\frac{M_1}{M_2}}

. Substituting

t_Y = 15\text{ s}

,

t_{O_2} = 30\text{ s}

, and

M_{O_2} = 32\text{ g/mol}

gives

\frac{15}{30} = \sqrt{\frac{M_Y}{32}}

. Squaring both sides yields

\frac{1}{4} = \frac{M_Y}{32}

, which simplifies to

M_Y = 8\text{ g/mol}

.

Step-by-Step Solution

1

State Graham's Law of Effusion relating effusion time (

t

) to molar mass (

M

).

\frac{t_Y}{t_{O_2}} = \sqrt{\frac{M_Y}{M_{O_2}}}

Effusion time for a fixed volume of gas is directly proportional to the square root of its molar mass because rate of effusion is inversely proportional to time.

2

Substitute the given values into the equation.

\frac{15}{30} = \sqrt{\frac{M_Y}{32}} \implies 0.5 = \sqrt{\frac{M_Y}{32}}

Given

t_Y = 15\text{ s}

,

t_{O_2} = 30\text{ s}

, and

M_{O_2} = 32\text{ g/mol}

.

3

Square both sides of the equation to eliminate the square root.

(0.5)^2 = \frac{M_Y}{32} \implies 0.25 = \frac{M_Y}{32}

Squaring isolates the ratio of molar masses.

4

Solve for

M_Y

.

M_Y = 0.25 \times 32 = 8\text{ g/mol}

Multiplying both sides by

32\text{ g/mol}

yields the molar mass of gas

Y

.

Key Concept

Graham's Law of Diffusion and Effusion relating time of effusion to molar mass

Question 6584Question →

Read the following prose excerpt carefully:

"The dust was relentless, sifting through the cracked wooden shutters and coating every surface in the cramped room with a fine, orange powder. Outside, the midday heat pressed down on the deserted street of the mining settlement, where the silence was broken only by the rhythmic, metallic clatter of the conveyor belt in the distance."

Which of the following best describes the prevailing atmosphere established in the excerpt?

A serene and tranquil rural setting detached from human labor.

An oppressive and desolate atmosphere reflecting harsh industrial living conditions.

A vibrant and celebratory mood amidst rapid urban development.

A mysterious and supernatural atmosphere within an isolated fortress.

Show answer & explanation

Answer: An oppressive and desolate atmosphere reflecting harsh industrial living conditions.

Answer

An oppressive and desolate atmosphere reflecting harsh industrial living conditions.

The imagery of relentless dust invading the cramped room, intense midday heat on a deserted street, and the monotonous metallic clatter of mining equipment collectively creates a mood of bleakness, heavy confinement, and harsh industrial living conditions.

Step-by-Step Solution

1

Analyze the physical setting details and sensory imagery in the prose passage.

The text highlights 'relentless' dust, a 'cramped room', 'midday heat pressing down', a 'deserted street', and the distant 'metallic clatter' of a mining conveyor belt.

Sensory descriptions of physical surroundings provide the direct evidence needed to infer atmosphere.

2

Synthesize the sensory details to infer the overall mood created for the reader.

The accumulation of claustrophobic dust, intense heat, solitude, and mechanical noise evokes feelings of bleakness, heaviness, and hardship.

Atmosphere refers to the emotional mood or aura created by the author's description of setting.

3

Evaluate the options against the synthesized mood.

The option identifying an oppressive and desolate industrial atmosphere accurately captures both the physical environment and the emotional tone.

It aligns fully with the textual evidence of physical discomfort and solitude in a mining outpost.

Key Concept

Atmosphere and Setting in Prose

Estimated Time:1m 15s

Question 6585Question →

A narrow beam containing $\alpha$ -particles, $\beta^-$ -particles, and $\gamma$ -rays enters a region of uniform magnetic field acting perpendicularly into the plane of the paper. If all three emissions enter with the same speed, which of the following observations correctly describes their paths in the magnetic field?

The

\beta^-

-particles curve more sharply than the

\alpha

-particles and in the opposite direction, while

\gamma

-rays continue straight without deflection.

The

\alpha

-particles curve more sharply than the

\beta^-

-particles in the opposite direction, while

\gamma

-rays are deflected parallel to the magnetic field.

Both

\alpha

-particles and

\beta^-

-particles curve in the same direction, but the

\alpha

-particles undergo a larger deflection due to their

+2e

charge.

The

\gamma

-rays curve towards the negative region while

\alpha

-particles and

\beta^-

-particles travel straight through without deflection.

Show answer & explanation

Answer: The $\beta^-$ -particles curve more sharply than the $\alpha$ -particles and in the opposite direction, while $\gamma$ -rays continue straight without deflection.

Answer

The beta-minus particles curve more sharply than the alpha particles and in the opposite direction, while gamma rays continue straight without deflection.

The magnetic force on a moving charged particle supplies the necessary centripetal force (

qvB = \frac{mv^2}{r}

), yielding a radius of curvature of

r = \frac{mv}{qB}

. Because a beta-minus particle has an extremely small mass compared to an alpha particle, its mass-to-charge ratio is much lower, resulting in a much tighter (sharper) circular arc. Because alpha particles are positively charged and beta-minus particles are negatively charged, they experience forces in opposite directions. Gamma rays have no charge and are therefore unaffected by the magnetic field.

Step-by-Step Solution

1

Identify the charge and mass characteristics of each emission type

Alpha particles (

\alpha

) have charge

+2e

and large mass (

\approx 4\text{ u}

). Beta-minus particles (

\beta^-

) have charge

-1e

and extremely small mass (

\approx 0.00055\text{ u}

). Gamma rays (

\gamma

) carry zero charge and zero rest mass.

Magnetic forces depend on moving charge (

F = qvB

), while inertia against trajectory changes depends on mass.

2

Determine deflection directions for each emission

Alpha particles (positive) and beta-minus particles (negative) deflect in opposite directions. Gamma rays (neutral) experience zero magnetic force and travel in a straight line.

Particles with opposite sign charges experience magnetic Lorentz forces in opposite directions.

3

Compare curvature extent using the magnetic radius formula

r = \frac{mv}{qB}

The mass-to-charge ratio

\frac{m}{q}

for

\beta^-

is far smaller than that for

\alpha

. Consequently,

r_{\beta} \ll r_{\alpha}

, meaning the

\beta^-

trajectory forms a tighter, sharper curve.

A smaller radius of curvature corresponds to a sharper trajectory deflection in the magnetic field.

Key Concept

Deflection and Curvature of Radioactive Radiation in Magnetic Fields

Question 6586Question →

A mixture of hexane (density $= 0.66\text{ g/cm}^3$ ) and an aqueous sodium chloride solution (density $= 1.05\text{ g/cm}^3$ ) is poured into a separating funnel. After shaking and allowing the mixture to settle into two distinct liquid layers, which of the following statements correctly identifies the bottom layer and the primary principle enabling this separation?

The aqueous sodium chloride solution forms the bottom layer because it is denser and immiscible with hexane.

Hexane forms the bottom layer because it has a lower boiling point than the aqueous sodium chloride solution.

The aqueous sodium chloride solution forms the bottom layer because it has a lower boiling point than hexane.

Hexane forms the bottom layer because it is less dense than the aqueous sodium chloride solution.

Show answer & explanation

Answer: The aqueous sodium chloride solution forms the bottom layer because it is denser and immiscible with hexane.

Answer

The aqueous sodium chloride solution forms the bottom layer because it is denser and immiscible with hexane.

A separating funnel is used to separate two immiscible liquids based on their density differences. Hexane (a non-polar organic liquid) and an aqueous sodium chloride solution (a polar liquid) do not mix. Since the aqueous solution has a greater density (

1.05\text{ g/cm}^3

) than hexane (

0.66\text{ g/cm}^3

), it sinks to form the lower layer, which can then be drained through the tap.

Step-by-Step Solution

1

Identify the physical properties required for separating funnel extraction.

Separating funnels require two immiscible liquids that separate into distinct phases.

Hexane is a non-polar organic solvent, while water/aqueous solution is polar, making them immiscible.

2

Compare the densities of the two immiscible liquids.

Aqueous NaCl solution (

1.05\text{ g/cm}^3

) is denser than hexane (

0.66\text{ g/cm}^3

).

Gravity causes the liquid with the higher density to sink to the bottom of the funnel.

3

Determine the bottom layer.

The denser aqueous NaCl solution settles at the bottom, while the less dense hexane forms the top layer.

Layer order in a separating funnel is strictly governed by density difference and immiscibility.

Key Concept

Separating Funnel Principles: Immiscibility and Density

Estimated Time:1m 0s

Question 6587Question →

Match each ground for partnership dissolution with its corresponding legal scenario or statutory circumstance under commercial law.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Dissolution by Operation of Law matches automatic termination due to bankruptcy or illegality; Dissolution by Notice matches unilateral termination in a partnership at will; Dissolution by Decree of Court matches forced judicial winding-up for persistent breach or incapacity; Dissolution by Expiration of Term matches natural termination upon completion of a specific project.

Each mode of dissolution aligns with a distinct legal trigger under partnership law: operation of law covers automatic termination via bankruptcy or illegal business; notice applies to partnerships at will; court decrees deal with serious misconduct or incapacity; and expiration of term applies to fixed-period or single-adventure partnerships.

Step-by-Step Solution

1

Identify the criteria for automatic statutory dissolution (Operation of Law).

Bankruptcy of a partner or an event making the business illegal automatically terminates the partnership.

Commercial law prohibits carrying on a partnership with an insolvent partner or for an illegal purpose.

2

Examine how a partnership at will is terminated by notice.

A partner can terminate an open-ended partnership by serving notice to the other partners.

Partnerships lacking a fixed term depend on the ongoing mutual agreement of all partners.

3

Distinguish judicial dissolution from non-judicial dissolution.

Courts grant a decree of dissolution when requested due to severe partner misconduct or permanent insanity.

Judicial intervention is necessary when internal resolution fails and legal compulsion is required.

4

Analyze event-based or temporal dissolution.

Completion of a single undertaking or reaching an agreed target date ends the partnership automatically.

The contractual life of the firm expires when its defining goal or period is fulfilled.

Key Concept

Grounds and Legal Modes of Partnership Dissolution

Question 6588Question →

Read the dramatic excerpt below carefully:

AGBA: (Pacing across the deserted marketplace as the storm approaches)
If I reveal the council's secret decree before dawn, the village will burn by my brother's torch. Yet if I remain silent, innocence perishes under the weight of false testimony. The gods demand a sacrifice, but they leave the executioner unnamed!

Which dramatic element is primarily illustrated by Agba's situation in this scene?

Crisis, as the character faces a pivotal dilemma that forces an impending decision.

An aside, because the character delivers a short comment directed to the audience while other characters remain present.

Dramatic irony, because the audience is kept completely unaware of the secret decree.

Tragic flaw, because the impending disaster is caused entirely by an external environmental event.

Show answer & explanation

Answer: Crisis, as the character faces a pivotal dilemma that forces an impending decision.

Answer

Crisis, as the character faces a pivotal dilemma that forces an impending decision.

The correct response identifies the crisis element of dramatic structure. Agba is at a critical juncture where opposing forces and moral choices collide, requiring a decisive resolution that will drive the rest of the plot toward its climax.

Step-by-Step Solution

1

Analyze the dramatic context provided in the excerpt.

The stage direction indicates that the character Agba is alone in a deserted marketplace, expressing intense internal conflict.

Understanding the physical setup and state of mind helps identify structural function.

2

Evaluate the nature of Agba's speech.

Agba is caught between two equally devastating choices (exposing the decree vs. remaining silent), creating a turning dilemma.

In dramatic structure, the crisis represents the peak of conflict where the protagonist must decide on a course of action leading directly to the climax.

Key Concept

Dramatic Structure - Crisis and Internal Conflict

Question 6589Question →

Calculate the percentage by mass of calcium in a pure sample of calcium carbonate ( $\text{CaCO}_3$ ). $[\text{Ca} = 40, \text{C} = 12, \text{O} = 16]$

Show answer & explanation

Answer: 40

Answer

The percentage by mass of calcium in calcium carbonate is 40%.

The molar mass of calcium carbonate (

\text{CaCO}_3

) is

100\text{ g/mol}

. Since one formula unit contains

40\text{ g}

of calcium, the percentage composition by mass of calcium is

\frac{40}{100} \times 100\% = 40\%

.

Step-by-Step Solution

1

Calculate the molar mass of calcium carbonate (

\text{CaCO}_3

).

Molar mass =

40 + 12 + (3 \times 16) = 100\text{ g/mol}

.

Sum the relative atomic masses of all constituent atoms in one formula unit of

\text{CaCO}_3

.

2

Determine the mass contribution of calcium in one mole of

\text{CaCO}_3

.

Mass of Ca =

40\text{ g}

.

Each formula unit of

\text{CaCO}_3

contains 1 atom of calcium.

3

Calculate the percentage composition of calcium.

Percentage of Ca =

\frac{40}{100} \times 100\% = 40\%

.

Divide the mass of calcium by the total molar mass of the compound and multiply by 100.

Key Concept

Percentage composition of an element in a compound

Question 6590Question →

A pure liquid sample held at its boiling point absorbs heat until it completely transforms into a gas at constant temperature and pressure. According to the Kinetic Molecular Theory of matter, what occurs to the average kinetic energy and the potential energy of the molecules during this phase change?

The average kinetic energy remains unchanged, while the potential energy increases as work is done against intermolecular forces of attraction.

Both the average kinetic energy and the potential energy increase simultaneously because thermal energy is continuously added to the system.

The average kinetic energy increases, but the potential energy remains constant because phase changes depend only on molecular speed.

The average kinetic energy decreases to compensate for the sharp increase in potential energy required to overcome intermolecular forces.

Show answer & explanation

Answer: The average kinetic energy remains unchanged, while the potential energy increases as work is done against intermolecular forces of attraction.

Answer

The average kinetic energy remains unchanged, while the potential energy increases as work is done against intermolecular forces of attraction.

According to the Kinetic Molecular Theory, absolute temperature is a direct measure of average kinetic energy. During boiling, temperature remains constant, so the average kinetic energy of the particles does not change. Instead, the heat energy added goes entirely into doing work to break intermolecular forces of attraction, increasing the potential energy as molecules transition from the liquid state to the gaseous state.

Step-by-Step Solution

1

Relate absolute temperature to kinetic energy using KMT postulates.

Since the phase transition occurs at a constant boiling temperature (

T

), the average kinetic energy (

E_k = \frac{3}{2}kT

) of the molecules remains strictly constant.

Postulates of the Kinetic Molecular Theory explicitly state that average kinetic energy is directly proportional to absolute temperature.

2

Analyze the role of absorbed heat during a phase change from liquid to gas.

The absorbed energy (latent heat of vaporization) is utilized exclusively to perform work against cohesive intermolecular forces.

Separating liquid molecules to the large intermolecular distances characteristic of gases increases the system's microscopic potential energy without changing temperature.

Key Concept

Phase Transitions, Intermolecular Forces, and Molecular Energy in KMT

Estimated Time:1m 30s

Question 6591Question →

Commercial banks provide various credit facilities and payment services designed to facilitate smooth trade transactions. Match each commercial banking service or payment instrument on the left with the specific operational requirement it fulfills for a trader on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Discounting Bills of Exchange matches selling an accepted trade bill to a bank before its due date at less than face value to obtain immediate liquidity; Credit Transfer matches remitting funds directly to multiple trade creditors' accounts across different financial institutions using a single payment instruction; Standing Order matches instructing a commercial bank to pay a fixed amount at regular specified intervals to a named beneficiary; Bank Overdraft matches allowing a current account holder to withdraw funds exceeding their account balance up to an agreed limit for short-term cash needs.

Each banking service directly aligns with its specific trade function: Discounting bills provides immediate cash before maturity; credit transfer simplifies bulk supplier payments; standing orders handle regular fixed commitments; overdrafts satisfy short-term working capital deficits.

Step-by-Step Solution

1

Analyze discounting bills of exchange

Identified as a short-term financing mechanism where a merchant receives immediate cash for a mature-dated trade bill by selling it to a bank at a fee.

This directly matches the definition of receiving liquidity prior to the maturity date of an accepted bill.

2

Analyze credit transfer mechanism

Identified as a bulk settlement service used by firms to pay several suppliers simultaneously via bank instructions.

This matches the bulk payment instruction method across multiple creditors.

3

Distinguish standing orders from direct debits

Identified standing order as customer-initiated fixed payments at regular intervals.

Standing orders specify fixed amounts paid regularly, unlike variable direct debits.

4

Evaluate bank overdraft features

Identified bank overdraft as a short-term temporary borrowing facility linked directly to a current account balance.

Overdrafts permit negative account balances up to an agreed threshold.

Key Concept

Commercial Banking Functions and Services to Trade

Question 6592Question →

A commercial bakery in Ibadan intends to divide its production into specialized workstations where individual workers handle single tasks exclusively. However, management discovers that local consumer demand is insufficient to absorb the output of continuous large-scale manufacturing. Which factor primarily limits the bakery's implementation of division of labour in this scenario?

The extent of market demand

The decline in individual worker craftsmanship

The accumulation of external economies of scale

The reliance of workers on direct production methods

Show answer & explanation

Answer: The extent of market demand

Answer

The extent of market demand

The extent of market demand dictates how far a firm can break down its production process. When demand is low, producing goods in large quantities via specialization leads to overproduction and unsold stock, making division of labour inefficient and unviable.

Step-by-Step Solution

1

Analyze the production scenario described in the stem

The firm wants to specialize workers across continuous workstations, but consumer purchasing volume is too low.

Identifying the constraint prevents confusing operational consequences with structural preconditions.

2

Relate the constraint to established economic principles of specialization

Adam Smith's principle states that 'division of labour is limited by the extent of the market.'

Specialization creates large outputs of standardized goods; if market demand cannot absorb this volume, continuous division of labour becomes economically unviable.

Key Concept

Limitations of Division of Labour (Extent of the Market)

Question 6593Question →

Match each type of stock exchange speculator listed on the left with its correct operational description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Bull matches with the speculator who buys expecting prices to rise; Bear matches with the speculator who sells expecting prices to fall; Stag matches with the speculator who subscribes to new issues for immediate resale profit; Lame Duck matches with the speculator unable to meet settlement commitments.

Each speculator is accurately paired with their distinct market behavior: Bulls buy in anticipation of rising prices, Bears sell expecting falling prices, Stags target new issue subscriptions for fast listing profits, and Lame Ducks are speculators failing to meet settlement obligations.

Step-by-Step Solution

1

Identify market expectations for price movements.

Bulls expect optimistic/rising market trends, while Bears anticipate pessimistic/falling market trends.

This establishes the fundamental distinction between long and short speculative positions in capital market trading.

2

Distinguish primary market speculators from secondary market operators.

Stags focus on primary market new share issues to make quick resale gains, rather than trading existing securities.

Stagging specifically targets newly issued shares before or immediately after official listing.

3

Match default conditions on stock exchange commitments.

Lame Ducks represent defaulted speculators who failed to absorb market losses.

When market price movements go opposite to a speculator's forecast, failure to settle transactions classifies them as a Lame Duck.

Key Concept

Stock Exchange Speculators and Trading Operations

Estimated Time:1m 30s

Question 6594Question →

A solid substance of mass $0.50\text{ kg}$ at its melting point is supplied with thermal energy by an electric heater operating at a constant rate of $150\text{ W}$ . If it takes $4.0\text{ minutes}$ for the solid to melt completely without any change in temperature, what is the specific latent heat of fusion of the substance?

1.8 \times 10^4\text{ J kg}^{-1}

7.2 \times 10^4\text{ J kg}^{-1}

3.6 \times 10^4\text{ J kg}^{-1}

1.2 \times 10^3\text{ J kg}^{-1}

Show answer & explanation

Answer: $7.2 \times 10^4\text{ J kg}^{-1}$

Answer

The specific latent heat of fusion of the substance is

7.2 \times 10^4\text{ J kg}^{-1}

.

During a change of phase at constant temperature, the thermal energy supplied is used exclusively to weaken intermolecular bonds without increasing kinetic energy or temperature. The heat supplied is

Q = P \times t = 150\text{ W} \times 240\text{ s} = 36\,000\text{ J}

. Using

Q = mL

, the specific latent heat

L = \frac{Q}{m} = \frac{36\,000\text{ J}}{0.50\text{ kg}} = 7.2 \times 10^4\text{ J kg}^{-1}

.

Step-by-Step Solution

1

Convert the given heating duration into SI units (seconds).

t = 4.0\text{ minutes} = 4.0 \times 60\text{ s} = 240\text{ s}

.

Standard calculation of thermal energy requires time to be in seconds when power is given in Watts.

2

Calculate the total thermal energy supplied by the heater.

Q = P \times t = 150\text{ W} \times 240\text{ s} = 36\,000\text{ J} = 3.6 \times 10^4\text{ J}

.

Electrical energy supplied is completely converted into heat energy.

3

Apply the latent heat formula to find the specific latent heat of fusion.

L = \frac{Q}{m} = \frac{36\,000\text{ J}}{0.50\text{ kg}} = 72\,000\text{ J kg}^{-1} = 7.2 \times 10^4\text{ J kg}^{-1}

.

During a change of state at constant temperature, heat absorbed is given by

Q = mL

.

Key Concept

Latent Heat of Fusion

Estimated Time:1m 30s

Question 6595Question →

Match each prose excerpt on the left with the dominant setting, atmosphere, or socio-cultural context it establishes on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Each prose excerpt correctly aligns with its contextual descriptor based on sensory imagery, historical markers, and atmospheric tone.

Each excerpt contains specific textual clues—such as colonial administrative references, weather conditions like the harmattan, modern urban sounds, or class-based architectural details—that uniquely define its spatial, temporal, and socio-cultural environment.

Step-by-Step Solution

1

Analyze sensory details and socio-historical markers in each passage.

Identified colonial references in passage one, urban technological markers in passage two, seasonal weather markers in passage three, and class indicators in passage four.

Setting and atmosphere are determined by imagery, environmental conditions, and cultural context indicators.

2

Map each passage to its corresponding environment and mood descriptor.

Formed accurate pairings matching environmental evidence with descriptive categories.

Direct evidence from the passage supports the socio-cultural and physical setting classification.

Key Concept

Analysis of Setting, Atmosphere, and Socio-Cultural Context in Prose Narrative

Question 6596Question →

A crate is pulled along a smooth horizontal floor by a constant force of $80\text{ N}$ applied at an angle of $60^\circ$ to the horizontal. If the crate moves through a displacement of $15\text{ m}$ along the floor, what is the work done by the applied force?

600\text{ J}

1039\text{ J}

1200\text{ J}

300\text{ J}

Show answer & explanation

Answer: $600\text{ J}$

Answer

600\text{ J}

The work done by a constant force applied at an angle

\theta

to the direction of motion is given by

W = F s \cos\theta

. Substituting

F = 80\text{ N}

,

s = 15\text{ m}

, and

\cos(60^\circ) = 0.5

gives

W = 80 \times 15 \times 0.5 = 600\text{ J}

.

Step-by-Step Solution

1

Identify the given physical quantities

Force

F = 80\text{ N}

, displacement

s = 15\text{ m}

, angle

\theta = 60^\circ

Extract parameters required for the work formula.

2

Apply the work formula for a force at an angle

W = F s \cos\theta

Only the component of force parallel to the displacement does work on the object.

3

Substitute the values and compute the result

W = 80 \times 15 \times \cos(60^\circ) = 1200 \times 0.5 = 600\text{ J}

Calculates the effective work done by the applied force.

Key Concept

Work Done by a Constant Force at an Angle

Estimated Time:1m 0s

Question 6597Question →

Match each industrial process on the left with its corresponding primary separation technique on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Production of oxygen gas matches liquefaction followed by fractional distillation; Refining of crude oil matches fractional distillation based on hydrocarbon boiling point differences; Removal of suspended particulate impurities matches coagulation with alum followed by sand filtration; Recovery of sodium hydrogentrioxocarbonate(IV) matches filtration of precipitated solid crystals.

Industrial separation methods rely on specific physical property differences: atmospheric gases and crude oil fractions are separated by fractional distillation due to boiling point differences; suspended particles in water are settled via coagulation and filtered; and solid precipitate crystals in the Solvay process are separated from liquid by filtration.

Step-by-Step Solution

1

Analyze the industrial separation of atmospheric air into components.

Air consists of gases (

N_2

,

Ar

,

O_2

) with very low boiling points. Liquefying the mixture under high pressure and low temperature followed by fractional distillation enables their separation.

Fractional distillation separates miscible substances with distinct boiling points.

2

Analyze the refining process of petroleum (crude oil).

Crude oil is a complex liquid mixture of hydrocarbons separated into fractions (gasoline, kerosene, diesel) inside a fractionating column based on boiling point ranges.

Smaller hydrocarbon molecules vaporize and rise higher up the column than larger molecules with higher boiling points.

3

Examine the municipal water clarification process.

Alum (potassium aluminium sulfate) causes fine suspended mud particles to coagulate into heavy flocs, which are removed as the water passes through sand beds.

Coagulation aggregates fine particles so that mechanical filtration can physically trap them.

4

Determine how solid sodium hydrogentrioxocarbonate(IV) is isolated in the Solvay process.

NaHCO_3

has lower solubility than ammonium chloride in cold water, precipitating out as solid crystals that are separated from the solution by filtration.

Filtration is used to separate insoluble or precipitated solid products from liquid reaction mixtures.

Key Concept

Industrial Applications of Separation Methods

Question 6598Question →

Match each dramatic structural element on the left with its correct function in play progression on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Inciting Incident matches with the event that disrupts the initial status quo; Falling Action matches with the stage of plot progression following the climax; Catastrophe matches with the ultimate tragic unraveling or disastrous conclusion; Subplot matches with a secondary narrative sequence running parallel to the main action.

Inciting Incident initiates dramatic conflict, Falling Action handles post-climax de-escalation, Catastrophe marks the tragic final outcome, and Subplot functions as a parallel secondary narrative.

Step-by-Step Solution

1

Analyze the function of the Inciting Incident in plot structure.

It breaks the pre-existing equilibrium and starts the conflict.

Dramatic conflict requires a specific initiating event to launch the rising action.

2

Determine the role of Falling Action in Freytag's dramatic pyramid.

It succeeds the turning point (climax) and leads toward resolution.

Falling action de-escalates major plot tensions following the dramatic climax.

3

Define Catastrophe within classical dramatic structure.

It represents the final tragic denouement involving the downfall of the hero.

Catastrophe forms the conclusive stage of tragic plot resolution.

4

Evaluate the structural utility of a Subplot.

It is a secondary story arc that mirrors, contrasts, or supports the main action.

Subplots enrich the overall dramatic narrative and thematic complexity.

Key Concept

Dramatic Elements and Plot Structure

Question 6599Question →

Match each poetic extract below with the primary sound device it exemplifies.

Click a left item, then click its matching right item

Show answer & explanation

Answer

"The heavy iron gate creaked and slammed shut." matches Onomatopoeia; "The light of the fire is a sight in the night." matches Assonance; "Peter's pale pony pranced along the pathway." matches Alliteration; "The slick snake struck the thick stick." matches Consonance.

Each extract demonstrates a distinct musical device: the first uses sound-mimicking words (onomatopoeia); the second repeats internal vowel sounds (assonance); the third repeats initial consonant sounds (alliteration); and the fourth repeats ending consonant sounds (consonance).

Step-by-Step Solution

1

Analyze the first extract for sound-imitative words

Identified 'creaked' and 'slammed'

Words that mimic natural auditory effects exemplify onomatopoeia.

2

Examine vowel sound repetition in the second extract

Observed repeated long '/aɪ/' vowel sound across multiple words

Repetition of identical or similar vowel sounds within close proximity defines assonance.

3

Identify initial consonant repetitions in the third extract

Found recurring initial '/p/' sounds in 'Peter's pale pony pranced pathway'

The repetition of initial consonant sounds in nearby words is alliteration.

4

Detect terminal consonant sound patterns in the fourth extract

Identified repeated ending '/k/' sounds in 'slick', 'struck', 'thick', and 'stick'

Repetition of final consonant sounds without matching preceding vowels constitutes consonance.

Key Concept

Distinguishing poetic sound devices through auditory patterns (Onomatopoeia, Assonance, Alliteration, and Consonance).

Question 6600Question →

In the hydronium ion ( $H_3O^+$ ), the central oxygen atom is bonded to three hydrogen atoms and retains one lone pair of electrons. Based on the Valence Shell Electron Pair Repulsion (VSEPR) theory, what are the molecular shape and the hybridization state of the central oxygen atom in $H_3O^+$ ?

Tetrahedral shape with

sp^3

hybridization

Trigonal pyramidal shape with

sp^3

hybridization

Trigonal planar shape with

sp^2

hybridization

Bent shape with

sp^2

hybridization

Show answer & explanation

Answer: Trigonal pyramidal shape with $sp^3$ hybridization

Answer

Trigonal pyramidal shape with

sp^3

hybridization

The central oxygen atom in

H_3O^+

possesses four electron domains (three

\sigma

bonding pairs with hydrogen atoms and one lone pair). Four total domains result in a steric number of 4, requiring

sp^3

hybridization. Because one of the four tetrahedral positions is occupied by a lone pair rather than a bonded atom, the visual arrangement of the nuclei forms a trigonal pyramidal molecular geometry.

Step-by-Step Solution

1

Determine the total number of valence electron pairs (steric number) around the central oxygen atom in

H_3O^+

.

Oxygen contributes 6 valence electrons, each hydrogen contributes 1, and the

+1

positive charge subtracts 1 electron:

(6 + 3 - 1) = 8

valence electrons (4 electron pairs).

VSEPR theory requires calculating the steric number to determine hybridization and basic electron geometry.

2

Determine the hybridization state from the steric number.

Steric number = 4 (3 bonding pairs + 1 lone pair), which corresponds to

sp^3

hybridization.

Four electron domains require four hybrid orbitals formed by combining one

s

and three

p

atomic orbitals.

3

Differentiate between electron pair geometry and molecular geometry.

While the 4 electron pairs adopt a tetrahedral electron geometry, the arrangement of the 3 bonded atoms around the central oxygen produces a trigonal pyramidal molecular shape.

Molecular shape describes only the spatial arrangement of atomic nuclei, excluding lone pair positions.

Key Concept

VSEPR Theory and Molecular Hybridization

Estimated Time:1m 15s

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