All practice questions

Question 6761Question →

A cell supplies a current of $0.6\text{ A}$ when connected across a $2.0\text{ }\Omega$ resistor. When the resistor is replaced with a $5.0\text{ }\Omega$ resistor, the current supplied by the cell drops to $0.3\text{ A}$ . What is the internal resistance of the cell?

1.0\text{ }\Omega

0.0\text{ }\Omega

3.0\text{ }\Omega

0.5\text{ }\Omega

Show answer & explanation

Answer: $1.0\text{ }\Omega$

Answer

The internal resistance of the cell is

1.0\text{ }\Omega

.

The electromotive force (e.m.f.)

E

of a cell is given by

E = I(R + r)

, where

I

is the current,

R

is external resistance, and

r

is internal resistance. Setting up equations for both cases:

E = 0.6(2.0 + r)

and

E = 0.3(5.0 + r)

. Equating them gives

1.2 + 0.6r = 1.5 + 0.3r

, which simplifies to

0.3r = 0.3

, yielding

r = 1.0\text{ }\Omega

.

Step-by-Step Solution

1

Formulate the electromotive force equation for the first circuit setup

E = I_1(R_1 + r) = 0.6(2.0 + r) = 1.2 + 0.6r

The total voltage supplied by the cell equals the total current multiplied by the sum of external and internal resistance.

2

Formulate the electromotive force equation for the second circuit setup

E = I_2(R_2 + r) = 0.3(5.0 + r) = 1.5 + 0.3r

The cell's electromotive force

E

and internal resistance

r

remain unchanged despite changing the external resistor.

3

Equate both expressions for electromotive force and solve for internal resistance

1.2 + 0.6r = 1.5 + 0.3r \implies 0.3r = 0.3 \implies r = 1.0\text{ }\Omega

Equating the two expressions allows direct solution for the single unknown variable

r

.

Key Concept

Electromotive Force and Internal Resistance of Cells

Question 6762Question →

In a Young's double-slit experiment, the separation between two narrow slits is $0.40\text{ mm}$ and the interference pattern is observed on a screen placed $1.20\text{ m}$ away from the slits. If the distance between consecutive bright fringes on the screen is $1.80\text{ mm}$ , what is the wavelength of the light used in nanometers ( $\text{nm}$ )?

Show answer & explanation

Answer: 600

Answer

The wavelength of the light used is

600\text{ nm}

.

Using the Young's double-slit fringe spacing relation

\beta = \frac{\lambda D}{d}

, rearranging yields

\lambda = \frac{\beta d}{D}

. Substituting

\beta = 1.80 \times 10^{-3}\text{ m}

,

d = 4.0 \times 10^{-4}\text{ m}

, and

D = 1.20\text{ m}

gives

\lambda = 6.00 \times 10^{-7}\text{ m}

, which corresponds to

600\text{ nm}

.

Step-by-Step Solution

1

Convert given physical quantities into standard SI units (meters).

Slit separation

d = 0.40\text{ mm} = 4.0 \times 10^{-4}\text{ m}

, distance to screen

D = 1.20\text{ m}

, and fringe spacing

\beta = 1.80\text{ mm} = 1.80 \times 10^{-3}\text{ m}

.

Standard SI units ensure accuracy when applying wave speed and distance equations.

2

Write the Young's double-slit formula relating fringe width to wavelength.

\beta = \frac{\lambda D}{d}

This relationship defines the spatial period of interference fringes on a screen.

3

Rearrange the equation to isolate the wavelength

\lambda

.

\lambda = \frac{\beta d}{D}

The unknown parameter to solve for is the wavelength of the monochromatic source.

4

Substitute the numerical values and convert the final result to nanometers.

$\lambda = \frac{1.80 \times 10^{-3}\text{ m} \times 4.0 \times 10^{-4}\text{ m}}{1.20\text{ m}} = 6.00 \times 10^{-7}\text{ m} = 600\text{ nm}$

Multiply meters by

10^9

to express the wavelength in nanometers.

Key Concept

Young's Double-Slit Interference Fringe Spacing

Question 6763Question →

In Isidore Okpewho's novel *The Last Duty*, what is Chief Toje's primary underlying motive for offering financial support and assistance to Aku while her husband is imprisoned?

To exploit her economic vulnerability to assert dominance and attempt to restore his failing sexual potency

To fulfill a moral obligation owed to Oshevire from a past commercial partnership prior to the outbreak of war

To secretly gather military intelligence regarding Rebel movements through her contacts across the border

To protect her from public scandal after she is accused of stealing relief materials from the local camp

Show answer & explanation

Answer: To exploit her economic vulnerability to assert dominance and attempt to restore his failing sexual potency

Answer

Chief Toje's primary motive is to exploit Aku's economic vulnerability to satisfy his own ego and attempt to prove his restored sexual potency.

In Isidore Okpewho's *The Last Duty*, Chief Toje's outward generosity toward Aku is driven by selfish psychological and sexual motives. Suffering from lost pride and physical impotence, he uses financial aid to coercion-trap the destitute Aku into sexual favors to bolster his ego.

Step-by-Step Solution

1

Analyze character relationships and conflicts in *The Last Duty*.

Identify Chief Toje as the antagonist who engineered Mukoro Oshevire's imprisonment on false charges of treason during the Nigerian Civil War.

Understanding the backstory clarifies the dynamic between Chief Toje and Oshevire's stranded wife, Aku.

2

Examine Chief Toje's inner monologues and interactions with Aku.

Recognize that Toje suffers from psychological anxiety over his declining physical health and sexual impotence, viewing Aku as a means to reassert his masculinity and dominance.

Toje's help is self-serving rather than altruistic, aimed at taking advantage of Aku's helplessness and social isolation.

Key Concept

Character Motivation and Moral Conflict in *The Last Duty*

Question 6764Question →

A uniform rigid bar $AB$ of length $2.0\text{ m}$ and weight $120\text{ N}$ is hinged smoothly at end $A$ to a vertical post. The bar is held in equilibrium at an angle of $60^\circ$ above the horizontal by a force $F$ applied at end $B$ acting perpendicular to the bar. What is the magnitude of the force $F$ ?

30\text{ N}

60\text{ N}

120\text{ N}

15\text{ N}

Show answer & explanation

Answer: $30\text{ N}$

Answer

The magnitude of the force required to keep the bar in equilibrium is

30\text{ N}

.

To maintain rotational equilibrium, the clockwise moment created by the weight of the bar about hinge

A

must equal the counterclockwise moment created by force

F

. The weight of

120\text{ N}

acts at the bar's midpoint (

1.0\text{ m}

from

A

), and its perpendicular distance to the vertical line of action is

1.0 \cos(60^\circ) = 0.5\text{ m}

. Thus, the clockwise moment is

120 \times 0.5 = 60\text{ N}\cdot\text{m}

. Since force

F

acts perpendicularly at the end of the

2.0\text{ m}

bar, its moment is

F \times 2.0

. Setting

2.0 F = 60

gives

F = 30\text{ N}

.

Step-by-Step Solution

1

Identify the center of gravity and the position of applied forces.

For a uniform bar of length

L = 2.0\text{ m}

, its weight

W = 120\text{ N}

acts vertically downward at its center of gravity, which is at a distance of

1.0\text{ m}

from hinge

A

.

The weight of a uniform body acts through its midpoint.

2

Determine the perpendicular distance for each force relative to the pivot at

A

.

Perpendicular distance for weight:

d_W = 1.0\text{ m} \times \cos(60^\circ) = 0.5\text{ m}

. Perpendicular distance for force

F

:

d_F = 2.0\text{ m}

(since

F

is perpendicular to the bar).

The moment of a force is defined as the product of the force magnitude and the perpendicular distance from the pivot to the line of action of the force.

3

Apply the Principle of Moments about the pivot

A

.

\sum M_A = 0 \implies F \times 2.0\text{ m} = 120\text{ N} \times 0.5\text{ m} \implies 2.0 F = 60 \implies F = 30\text{ N}

.

For rotational equilibrium, the total counterclockwise moment about any pivot must equal the total clockwise moment.

Key Concept

Principle of Moments and Rotational Equilibrium

Question 6765Question →

Under the legal principle of proximate cause in insurance, an insurer is liable for loss or damage if the direct, dominant, and efficient cause that set the chain of events in motion is an insured peril, even if an intermediate event in the sequence was not specifically named in the policy.

True

False

Show answer & explanation

Answer: True

Answer

True. The principle of proximate cause states that an insurer is liable when an insured peril is the dominant, efficient cause that initiates an unbroken sequence of events leading to a loss.

The statement accurately reflects the principle of proximate cause (causa proxima). In commercial insurance, the proximate cause is not necessarily the closest event in time to the damage, but the active, dominant, and efficient cause that set the unbroken chain of events into motion. If the originating cause is a peril insured against, the insurer is legally responsible for the loss.

Step-by-Step Solution

1

Define the legal principle of proximate cause (causa proxima) in insurance.

Proximate cause refers to the direct, effective, and dominant cause that sets in motion a continuous chain of events leading to damage, without the intervention of an independent new force.

Insurance claims evaluate legal liability based on the primary initiating cause rather than merely the last or remote event in time.

2

Apply the principle to uninterrupted sequences involving covered perils.

If an insured peril initiates an unbroken chain of consequences, all resulting losses directly linked to that initial peril are covered by the policy.

The law holds the insurer accountable for consequences arising naturally and directly from the insured hazard.

Key Concept

Principle of Proximate Cause (Causa Proxima)

Question 6766Question →

A $10.0\text{ g}$ sample of hydrated magnesium tetraoxosulfate(VI), $\text{MgSO}_4 \cdot x\text{H}_2\text{O}$ , is heated to constant mass in a crucible, leaving a residue of $4.88\text{ g}$ of anhydrous salt. When the anhydrous residue is exposed to moist ambient air at room temperature, it absorbs water vapor until its mass increases back to $10.0\text{ g}$ without forming a liquid solution. What is the integer value of $x$ , and what atmospheric behavior does the anhydrous salt display during moisture absorption? $[\text{Relative atomic masses: } \text{Mg} = 24, \text{S} = 32, \text{O} = 16, \text{H} = 1]$

x = 7

, and the salt displays hygroscopy

x = 7

, and the salt displays deliquescence

x = 5

, and the salt displays hygroscopy

x = 5

, and the salt displays efflorescence

Show answer & explanation

Answer: $x = 7$ , and the salt displays hygroscopy

Answer

x = 7

, and the salt displays hygroscopy

The mass of water lost from

10.0\text{ g}

of

\text{MgSO}_4 \cdot x\text{H}_2\text{O}

is

5.12\text{ g}

. Converting the mass of anhydrous

\text{MgSO}_4

(

4.88\text{ g}

) and water (

5.12\text{ g}

) to moles gives

0.04067\text{ mol}

and

0.2844\text{ mol}

respectively, yielding

x = 7

. Because the anhydrous salt absorbs atmospheric moisture without dissolving into a liquid solution, it demonstrates hygroscopy.

Step-by-Step Solution

1

Calculate the mass of water lost upon heating.

\text{Mass of } \text{H}_2\text{O} = 10.0\text{ g} - 4.88\text{ g} = 5.12\text{ g}

Heating to constant mass drives off all water of crystallization from the hydrated crystal structure.

2

Determine the molar masses of anhydrous

\text{MgSO}_4

and

\text{H}_2\text{O}

.

Molar mass of

\text{MgSO}_4 = 24 + 32 + (4 \times 16) = 120\text{ g/mol}

; Molar mass of

\text{H}_2\text{O} = (2 \times 1) + 16 = 18\text{ g/mol}

.

Required to convert sample masses into chemical mole quantities.

3

Calculate the mole ratio of water of crystallization to anhydrous salt to find

x

.

\text{Moles of } \text{MgSO}_4 = \frac{4.88}{120} = 0.04067\text{ mol}

;

\text{Moles of } \text{H}_2\text{O} = \frac{5.12}{18} = 0.2844\text{ mol}

;

x = \frac{0.2844}{0.04067} = 7

.

The coefficient

x

represents the integer ratio of moles of water to moles of anhydrous salt.

4

Identify the atmospheric behavior of the anhydrous salt upon absorbing moisture without forming a solution.

The behavior is termed hygroscopy (or hygroscopic nature).

Hygroscopic substances absorb moisture from air without forming a liquid solution, whereas deliquescent substances absorb enough moisture to dissolve into a solution.

Key Concept

Stoichiometric determination of water of crystallization and conceptual differentiation between hygroscopy and deliquescence.

Question 6767Question →

Match each chemical solute with its characteristic solubility curve behavior in water as temperature increases.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Potassium nitrate (

KNO_3

) matches with steep solubility increase; Sodium chloride (

NaCl

) matches with virtually constant solubility; Hydrated sodium sulfate (

Na_2SO_4 \cdot 10H_2O

) matches with an increase up to

32.4^\circ\text{C}

followed by a decrease; Calcium hydroxide (

Ca(OH)_2

) matches with decreasing solubility.

Each salt exhibits a specific relationship between temperature and solubility governed by its enthalpy of solution and hydration state. Potassium nitrate has a steep positive curve due to endothermic dissolution. Sodium chloride shows a flat curve due to negligible heat of solution. Hydrated sodium sulfate displays a sharp break at

32.4^\circ\text{C}

marking the transition to anhydrous

Na_2SO_4

. Calcium hydroxide shows a continuous drop in solubility because its dissolution is exothermic.

Step-by-Step Solution

1

Analyze the thermal effect of dissolution for endothermic salts with no phase transitions.

Potassium nitrate (

KNO_3

) absorbs substantial thermal energy upon dissolving, yielding a steep positive slope on a solubility graph.

According to Le Chatelier's principle, increasing temperature shifts endothermic dissolution equilibria toward increased solute dissolution.

2

Evaluate salts with negligible heats of solution.

Sodium chloride (

NaCl

) exhibits a nearly horizontal curve, showing minimal change in solubility over a wide temperature range.

The lattice energy and hydration energy of

NaCl

are nearly equal, resulting in negligible temperature dependence.

3

Identify salts undergoing chemical dehydration or phase changes.

Glauber's salt (

Na_2SO_4 \cdot 10H_2O

) shows a sudden sharp break (kink) at

32.4^\circ\text{C}

.

Below

32.4^\circ\text{C}

, the decahydrate dissolves endothermically. Above

32.4^\circ\text{C}

, it dehydrates to anhydrous

Na_2SO_4

, which dissolves exothermically.

4

Analyze exothermic dissolution processes.

Calcium hydroxide (

Ca(OH)_2

) exhibits a downward-sloping solubility curve.

Exothermic processes release heat upon dissolution; raising the temperature suppresses dissolution and causes precipitation.

Key Concept

Effect of Temperature and Enthalpy of Solution on Solubility Curves

Estimated Time:1m 30s

Question 6768Question →

Consider the balanced chemical equation for the complete combustion of ethane gas:

2C_2H_6(g) + 7O_2(g) \rightarrow 4CO_2(g) + 6H_2O(g)

What volume of oxygen gas, measured at STP, is required to react completely with

0.5\text{ mol}

of ethane? Complete the statement below with the calculated numerical value.

Fill in the blanks below

The volume of oxygen gas required at STP is

\text{dm}^3

. (Molar gas volume at STP =

22.4\text{ dm}^3\text{mol}^{-1}

)

Show answer & explanation

Answer

39.2 dm³ (or 39.2)

According to the balanced equation

2C_2H_6(g) + 7O_2(g) \rightarrow 4CO_2(g) + 6H_2O(g)

,

2\text{ moles}

of ethane require

7\text{ moles}

of oxygen gas for complete combustion. Therefore,

0.5\text{ mol}

of ethane requires

\frac{0.5 \times 7}{2} = 1.75\text{ mol}

of oxygen gas. At standard temperature and pressure (STP),

1\text{ mole}

of gas occupies

22.4\text{ dm}^3

. Thus, the volume of oxygen gas required is

1.75\text{ mol} \times 22.4\text{ dm}^3\text{mol}^{-1} = 39.2\text{ dm}^3

.

Step-by-Step Solution

1

Identify the stoichiometric mole ratio between ethane and oxygen from the balanced equation

From

2C_2H_6 + 7O_2

, the mole ratio of

C_2H_6

to

O_2

is

2 : 7

.

Stoichiometric coefficients represent the relative mole proportions of reactants.

2

Calculate the moles of oxygen gas needed for 0.5 mol of ethane

Moles of

O_2 = 0.5\text{ mol} \times \frac{7}{2} = 1.75\text{ mol}

Multiplying the given amount of ethane by the stoichiometric factor gives the required moles of oxygen.

3

Convert the calculated moles of oxygen gas to volume at STP

Volume of

O_2 = 1.75\text{ mol} \times 22.4\text{ dm}^3\text{mol}^{-1} = 39.2\text{ dm}^3

One mole of any ideal gas occupies

22.4\text{ dm}^3

at STP.

Key Concept

Mole-Volume Stoichiometric Calculations at STP

Question 6769Question →

A light ray travels from Medium X into Medium Y. The speed of light in Medium X is $1.50 \times 10^8\text{ m/s}$ and the speed of light in Medium Y is $2.50 \times 10^8\text{ m/s}$ . What is the sine of the critical angle for total internal reflection at the boundary between these two media?

0.60

1.67

0.50

0.40

Show answer & explanation

Answer: $0.60$

Answer

The sine of the critical angle for total internal reflection at the boundary is

0.60

.

Total internal reflection occurs when light moves from an optically denser medium to an optically less dense medium. By Snell's law,

n_X \sin\theta_c = n_Y \sin 90^\circ

, which gives

\sin\theta_c = n_Y / n_X

. Since refractive index is inversely proportional to speed (

n = c/v

),

\sin\theta_c = v_X / v_Y = (1.50 \times 10^8) / (2.50 \times 10^8) = 0.60

.

Step-by-Step Solution

1

Relate speed of light in each medium to their respective refractive indices

n_X = \frac{c}{v_X}

and

n_Y = \frac{c}{v_Y}

Refractive index is defined as the ratio of light speed in vacuum to light speed in the medium.

2

Apply Snell's Law for the critical angle condition

\sin\theta_c = \frac{n_Y}{n_X}

At the critical angle, the angle of refraction in the less dense medium is

90^\circ

(

\sin 90^\circ = 1

).

3

Substitute light speeds into the critical angle formula and calculate

\sin\theta_c = \frac{v_X}{v_Y} = \frac{1.50 \times 10^8\text{ m/s}}{2.50 \times 10^8\text{ m/s}} = 0.60

Substituting the expressions for

n_X

and

n_Y

simplifies the refractive index ratio to the direct ratio of speeds

v_X / v_Y

.

Key Concept

Critical angle and total internal reflection relation to speed of light in media

Question 6770Question →

A commercial firm secures an insurance policy to safeguard its business against pecuniary losses arising from fraud, embezzlement, or dishonest acts committed by its cash-handling employees. Which type of insurance policy has the firm acquired?

Fidelity Guarantee policy

Employer's Liability policy

Endowment Assurance policy

Reinsurance policy

Show answer & explanation

Answer: Fidelity Guarantee policy

Answer

Fidelity Guarantee policy

A Fidelity Guarantee policy is a form of accident insurance designed specifically to protect employers against financial loss caused by fraudulent or dishonest acts of employees, such as cashiers, accountants, or storekeepers.

Step-by-Step Solution

1

Analyze the nature of the risk described in the scenario

The risk involves pecuniary (financial) loss resulting from internal employee dishonesty, fraud, or theft.

Identifying the specific cause of potential loss determines the corresponding insurance policy classification.

2

Match the risk type to the relevant accident insurance policy

Fidelity Guarantee insurance covers losses caused by breach of trust or fraud committed by employees in trusted roles.

This policy is specifically designed for businesses to mitigate risks associated with staff handling cash, stock, or financial records.

Key Concept

Fidelity Guarantee Policy Coverage

Estimated Time:1m 0s

Question 6771Question →

In a metre bridge experiment, a standard resistor of $4.0\text{ }\Omega$ is connected in the left gap and an unknown resistor $R$ is connected in the right gap. When balanced, the balance point is found at a distance of $40.0\text{ cm}$ from the left end of the $100.0\text{ cm}$ bridge wire. What is the value of the unknown resistance $R$ in ohms?

Show answer & explanation

Answer: 6

Answer

The value of the unknown resistance

R

is

6.0\text{ }\Omega

.

The metre bridge operates on the Wheatstone bridge principle. At balance, the ratio of the resistance in the left gap to the length of the left segment equals the ratio of the resistance in the right gap to the length of the right segment. Substituting

4.0\text{ }\Omega

for the left gap and

40.0\text{ cm}

and

60.0\text{ cm}

for the two wire lengths yields

R = 6.0\text{ }\Omega

.

Step-by-Step Solution

1

Determine the length of the wire segment corresponding to the right gap.

l_2 = 100.0\text{ cm} - 40.0\text{ cm} = 60.0\text{ cm}

.

The total length of a standard metre bridge wire is

100.0\text{ cm}

.

2

Apply the Wheatstone bridge principle for the metre bridge balance condition.

\frac{R_{\text{left}}}{l_1} = \frac{R}{l_2} \implies R = R_{\text{left}} \times \frac{l_2}{l_1}

.

At balance, the potential drop per unit length across the two wire segments is proportional to their respective lengths.

3

Calculate the magnitude of the unknown resistor

R

.

R = 4.0 \times \frac{60.0}{40.0} = 6.0\text{ }\Omega

.

Multiplying and simplifying yields the exact resistance value.

Key Concept

Metre Bridge Principle (Wheatstone Bridge)

Question 6772Question →

Match each operational function of a merchant wholesaler listed on the left with its corresponding description or benefit on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Bulk breaking corresponds to dividing large factory consignments into manageable packages for retailers. Market intelligence corresponds to relaying customer feedback and demand trends back to manufacturers. Financing production corresponds to making prompt cash payments and placing advance orders with manufacturers. Credit extension corresponds to allowing small retail traders to purchase goods and settle payments later.

Wholesalers serve as vital channel intermediaries. Bulk breaking allows small retailers to buy convenient quantities; market intelligence keeps producers informed of consumer trends; financing production ensures steady manufacturing operations; and credit extension helps small retailers manage working capital.

Step-by-Step Solution

1

Analyze functions performed primarily for producers versus retailers

Identified 'Financing production' and 'Market intelligence' as services rendered to manufacturers, while 'Bulk breaking' and 'Credit extension' are services rendered to retailers.

Wholesalers act as intermediaries serving two distinct groups in the distribution channel.

2

Match producer-directed functions to their descriptions

Paired 'Market intelligence' with relaying feedback to manufacturers, and 'Financing production' with prompt cash advances and orders.

Producers rely on wholesalers for capital flow and market demand insights.

3

Match retailer-directed functions to their descriptions

Paired 'Bulk breaking' with packaging smaller units, and 'Credit extension' with deferred payment terms for retailers.

Retailers usually operate with small working capital and cannot handle factory-sized consignments.

Key Concept

Dual Functions of Wholesalers to Manufacturers and Retailers

Question 6773Question →

Sodium hydrogentrioxocarbonate(IV) decomposes upon heating according to the balanced chemical equation:

2NaHCO_3(s) \rightarrow Na_2CO_3(s) + H_2O(l) + CO_2(g)

What mass of sodium trioxocarbonate(IV) (

Na_2CO_3

) is produced by the complete decomposition of

16.8\text{ g}

of

NaHCO_3

?

[Na = 23, C = 12, O = 16, H = 1]

10.6\text{ g}

21.2\text{ g}

4.4\text{ g}

42.4\text{ g}

Show answer & explanation

Answer: $10.6\text{ g}$

Answer

The mass of sodium trioxocarbonate(IV) produced is

10.6\text{ g}

.

The complete decomposition of

16.8\text{ g}

(

0.20\text{ mol}

) of

NaHCO_3

produces

0.10\text{ mol}

of

Na_2CO_3

according to the

2:1

mole ratio in the balanced equation. Multiplying

0.10\text{ mol}

by the molar mass of

Na_2CO_3

(

106\text{ g mol}^{-1}

) gives

10.6\text{ g}

.

Step-by-Step Solution

1

Calculate the molar masses of

NaHCO_3

and

Na_2CO_3

Molar mass of

NaHCO_3 = 23 + 1 + 12 + 3(16) = 84\text{ g mol}^{-1}

. Molar mass of

Na_2CO_3 = 2(23) + 12 + 3(16) = 106\text{ g mol}^{-1}

.

Molar masses are required to convert between mass and mole amounts.

2

Determine the number of moles of

NaHCO_3

reacted

\text{Moles of } NaHCO_3 = \frac{16.8\text{ g}}{84\text{ g mol}^{-1}} = 0.20\text{ mol}.

Stoichiometric relations are calculated using mole amounts rather than raw masses.

3

Use the mole ratio from the balanced chemical equation to find moles of

Na_2CO_3

From

2NaHCO_3 \rightarrow Na_2CO_3

, ratio is

2:1

. Therefore, \text{moles of } Na_2CO_3 = \frac{0.20}{2} = 0.10\text{ mol}.

Two moles of

NaHCO_3

produce one mole of

Na_2CO_3

.

4

Calculate the mass of

Na_2CO_3

produced

\text{Mass of } Na_2CO_3 = 0.10\text{ mol} \times 106\text{ g mol}^{-1} = 10.6\text{ g}.

Multiplying moles of product by its molar mass yields the theoretical yield mass.

Key Concept

Mass-Mass Stoichiometric Calculations

Estimated Time:1m 30s

Question 6774Question →

In a statutory public corporation established to manage a nation's electricity grid, day-to-day operations are handled by executive management. Which authority holds the statutory responsibility for formulating general policy directives and appointing members of the governing board?

The supervising government minister

The general public through annual general meetings

The managing director of the enterprise

The judicial council through court orders

Show answer & explanation

Answer: The supervising government minister

Answer

The supervising government minister holds the statutory authority to appoint board members and issue general policy directives to a public corporation.

The supervising minister represents the executive arm of government and exercises ministerial control over public enterprises. This oversight includes appointing members of the governing board, approving major capital expenditure projects, and issuing broad policy directives to align corporate activities with public interest.

Step-by-Step Solution

1

Analyze the management and control structure of statutory public enterprises.

Public corporations are owned by the government and created by an Act of Parliament to provide essential services.

Understanding the separation of ownership, policy control, and operational management is essential for identifying governing roles.

2

Distinguish between operational administration and ministerial control.

Executive management handles routine operations, while the supervising minister (executive government) appoints the Board of Directors and provides broad policy guidance.

Ministerial control ensures public corporations remain accountable to the government and align with national public interest objectives.

Key Concept

Ministerial Control of Public Enterprises

Question 6775Question →

In Bayo Adebowale's prescribed novel *Lonely Days*, how does Yaremi sustain herself financially and maintain her independence in Kufi village following the death of her husband, Ajumobi?

By producing and selling dyed fabrics, taffeta, and traditional adire materials

By receiving monthly financial stipends from her late husband's brothers during her mourning period

By taking over her late husband's former trade as a village hunter and selling bushmeat

By operating a sewing shop in the city with her eldest daughter, Segi

Show answer & explanation

Answer: By producing and selling dyed fabrics, taffeta, and traditional adire materials

Answer

Yaremi sustains herself and preserves her autonomy by producing and selling dyed fabrics (adire) in Kufi village.

In Bayo Adebowale's *Lonely Days*, Yaremi's trade as a fabric dyer producing colorful adire and taffeta is her primary source of financial sustenance. This economic stability gives her the strength and courage to refuse traditional widowhood pressure and remarriage to her late husband's brothers.

Step-by-Step Solution

1

Identify the protagonist's socio-economic role in Bayo Adebowale's novel *Lonely Days*.

Yaremi is depicted as an independent and hard-working widow in Kufi.

Characterization in the novel highlights her economic self-sufficiency despite widowhood traditions.

2

Recall Yaremi's specific trade and source of income following Ajumobi's death.

She works as a fabric dyer, making taffeta and adire to trade in the local market.

This economic independence enables her to resist unwanted remarriage proposals from Ajumobi's relatives.

Key Concept

Character resilience and economic independence in prescribed African prose

Estimated Time:1m 0s

Question 6776Question →

Match each character from Alex Agyei-Agyiri's prescribed African prose text, *Unexpected Joy at Dawn*, to their defining experience or thematic role within the novel.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Nii matches with the bank worker living as an alien in Ghana facing financial hardship, xenophobia, and political expulsion while seeking his sister. Mama Orojo matches with the prosperous Nigerian businesswoman who travels to Ghana to search for her long-lost brother while navigating religious and social challenges. Joe matches with the opportunistic gold prospector involved in illegal mining ventures who assists in reconnecting separated family members. Massa matches with the terminally ill woman whose physical deterioration and eventual death reflect the socio-political decay of the nation.

In Alex Agyei-Agyiri's *Unexpected Joy at Dawn*, Nii represents the displaced alien struggling under harsh economic conditions in Ghana. Mama Orojo is his wealthy sister operating in Nigeria who seeks him out. Joe is the gold miner who crosses paths with Mama Orojo, and Massa is Nii's ailing partner whose suffering symbolizes the nation's decline.

Step-by-Step Solution

1

Analyze the protagonist's identity and primary conflict in Unexpected Joy at Dawn.

Identify Nii as the main male protagonist struggling with xenophobic hostility and alien status in Ghana.

Nii's narrative arc centers on hardship in Ghana and his eventual escape to Nigeria.

2

Identify the primary female protagonist based in Nigeria.

Connect Mama Orojo to her business empire in Nigeria and her cross-border quest to locate Nii.

Mama Orojo's financial success in Illaro contrasts with Nii's poverty in Accra.

3

Examine key supporting characters and their symbolic or narrative functions.

Link Joe to gold prospecting (galamsey) and Massa to symbolic physical illness representing national decay.

Joe's mining activities drive the sub-plot of economic speculation, whereas Massa's illness mirrors Ghana's economic crisis.

Key Concept

Characterization and Thematic Roles in Prescribed African Novels

Estimated Time:1m 30s

Question 6777Question →

The solubility of a solute $X$ in water is $1.5\text{ mol/dm}^3$ at $80^\circ\text{C}$ and $0.5\text{ mol/dm}^3$ at $30^\circ\text{C}$ . If $250\text{ cm}^3$ of a saturated solution of $X$ at $80^\circ\text{C}$ is cooled to $30^\circ\text{C}$ , what mass of $X$ will crystallize out of the solution? [Molar mass of $X = 160\text{ g/mol}$ ]

40.0\text{ g}

160.0\text{ g}

0.25\text{ g}

60.0\text{ g}

Show answer & explanation

Answer: $40.0\text{ g}$

Answer

The mass of salt

X

that crystallizes out of solution is

40.0\text{ g}

.

Cooling

1\text{ dm}^3

of saturated solution from

80^\circ\text{C}

to

30^\circ\text{C}

precipitates

1.0\text{ mol}

of solute. For a

250\text{ cm}^3

(

0.25\text{ dm}^3

) solution,

0.25\text{ mol}

precipitates. Multiplying

0.25\text{ mol}

by the molar mass (

160\text{ g/mol}

) yields

40.0\text{ g}

.

Step-by-Step Solution

1

Calculate the difference in solubility between

80^\circ\text{C}

and

30^\circ\text{C}

per

\text{dm}^3

.

\Delta S = 1.5\text{ mol/dm}^3 - 0.5\text{ mol/dm}^3 = 1.0\text{ mol/dm}^3

Solubility decreases upon cooling, causing the excess solute to precipitate.

2

Scale the amount of precipitated solute to the specified volume of

250\text{ cm}^3

(

0.25\text{ dm}^3

).

n_{\text{precipitated}} = 1.0\text{ mol/dm}^3 \times 0.25\text{ dm}^3 = 0.25\text{ mol}

The solution volume is

250\text{ cm}^3

, which is a quarter of a cubic decimeter.

3

Convert the moles of precipitated solute to mass in grams using its molar mass.

\text{Mass} = 0.25\text{ mol} \times 160\text{ g/mol} = 40.0\text{ g}

Mass is obtained by multiplying the chemical amount in moles by the molar mass.

Key Concept

Calculation of mass crystallized from solubility curves and temperature changes

Question 6778Question →

A multinational firm in Nigeria manufactures mass-market laundry detergent designed for millions of individual households spread across both urban and rural regions. Which channel of distribution is most effective for achieving widespread market coverage for this type of fast-moving consumer good?

Producer → Wholesaler → Retailer → Consumer

Producer → Consumer

Producer → Agent → Consumer

Producer → Retailer → Consumer

Show answer & explanation

Answer: Producer → Wholesaler → Retailer → Consumer

Answer

The most effective channel of distribution is Producer → Wholesaler → Retailer → Consumer.

For low-unit-value, standardized, fast-moving consumer goods (FMCG) like laundry detergent aimed at millions of widely scattered households, a long distribution channel (Producer → Wholesaler → Retailer → Consumer) is required. The wholesaler performs the essential functions of breaking bulk and financing inventory, while localized retailers make small quantities conveniently accessible to consumers.

Step-by-Step Solution

1

Analyze the nature of the product and consumer base

Laundry detergent is a non-perishable, low-unit-value, fast-moving consumer good (FMCG) sold to millions of dispersed consumers.

Product characteristics determine the ideal length of the distribution channel.

2

Evaluate middleman requirements

Wholesalers are needed to purchase in bulk, store large inventories, and break bulk for small retailers. Retailers are needed to sell single units to household consumers.

Mass market coverage requires intensive distribution that a single producer cannot efficiently manage alone.

3

Select the optimal channel structure

Producer → Wholesaler → Retailer → Consumer provides the broadest reach at the lowest cost per unit sold.

This long channel minimizes transaction costs for high-volume, standardized consumer products.

Key Concept

Selection of Distribution Channels based on Product Characteristics and Market Scope

Question 6779Question →

A battery with an electromotive force (e.m.f.) of $9.0\text{ V}$ and an internal resistance of $0.5\text{ }\Omega$ is connected to an external circuit containing two resistors of $4.0\text{ }\Omega$ and $1.5\text{ }\Omega$ connected in series. What is the terminal potential difference across the battery?

8.25\text{ V}

9.00\text{ V}

0.75\text{ V}

6.00\text{ V}

Show answer & explanation

Answer: $8.25\text{ V}$

Answer

The terminal potential difference across the battery is

8.25\text{ V}

.

The correct answer is obtained by finding the total circuit resistance (

6.0\text{ }\Omega

), determining the current (

1.5\text{ A}

), and subtracting the internal voltage drop (

0.75\text{ V}

) from the electromotive force (

9.0\text{ V}

) to give

8.25\text{ V}

.

Step-by-Step Solution

1

Calculate the total resistance of the circuit.

R_{\text{total}} = R_1 + R_2 + r = 4.0\text{ }\Omega + 1.5\text{ }\Omega + 0.5\text{ }\Omega = 6.0\text{ }\Omega

The external resistors and the battery's internal resistance are connected in series.

2

Calculate the total current flowing through the circuit using Ohm's Law.

I = \frac{E}{R_{\text{total}}} = \frac{9.0\text{ V}}{6.0\text{ }\Omega} = 1.5\text{ A}

The total current depends on the electromotive force and total circuit resistance.

3

Calculate the terminal potential difference across the battery.

V = E - I r = 9.0\text{ V} - (1.5\text{ A} \times 0.5\text{ }\Omega) = 9.0\text{ V} - 0.75\text{ V} = 8.25\text{ V}

Terminal voltage is equal to the e.m.f. minus the potential drop across the internal resistance.

Key Concept

Terminal potential difference and internal resistance in DC electric circuits

Estimated Time:1m 30s

Question 6780Question →

Monochromatic light of wavelength $600\text{ nm}$ is incident normally on a diffraction grating having $500\text{ lines per mm}$ . What is the angle of diffraction, in degrees, for the first-order principal maximum?

Show answer & explanation

Answer: 17.5

Answer

The angle of diffraction for the first-order principal maximum is

17.5^\circ

.

Using the grating equation

d \sin \theta = n \lambda

, the slit separation is

d = \frac{10^{-3}\text{ m}}{500} = 2.00 \times 10^{-6}\text{ m}

. For

n = 1

and

\lambda = 6.00 \times 10^{-7}\text{ m}

, we get

\sin \theta = \frac{6.00 \times 10^{-7}}{2.00 \times 10^{-6}} = 0.30

. Taking

\arcsin(0.30)

gives approximately

17.5^\circ

.

Step-by-Step Solution

1

Calculate the grating element (slit spacing)

d

d = 2.00 \times 10^{-6}\text{ m}

Grating spacing

d

is the reciprocal of the line density

N = 500\text{ lines/mm} = 500,000\text{ lines/m}

.

2

Apply the diffraction grating equation

d \sin \theta = n \lambda

\sin \theta = 0.30

For the first-order maximum (

n = 1

),

\sin \theta = \frac{1 \times 600 \times 10^{-9}\text{ m}}{2.00 \times 10^{-6}\text{ m}} = 0.30

.

3

Find the angle

\theta

by taking the inverse sine

\theta = 17.5^\circ

\arcsin(0.30) \approx 17.46^\circ

, which rounds to

17.5^\circ

.

Key Concept

Diffraction Grating Equation for Principal Maxima

Estimated Time:1m 30s

Answer

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