All practice questions

Question 3061Question →

The human immune system utilizes multiple specialized components to prevent infection, eliminate pathogens, and maintain long-term protection. Match each immune defense component on the left with its corresponding physiological function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Phagocytes pair with non-specific engulfing and destruction of microorganisms; B lymphocytes pair with production of antigen-specific antibodies; Memory cells pair with long-term persistence for rapid secondary responses; Mucous membranes pair with physical and chemical barrier protection that traps pathogens.

Each immune component is correctly matched with its biological function: mucous membranes act as primary surface barriers to entrap pathogens, phagocytes conduct non-specific cellular ingestion, B lymphocytes synthesize antigen-specific antibodies, and memory cells preserve immunological memory for rapid secondary responses.

Step-by-Step Solution

1

Classify the first-line mechanical and chemical defense mechanisms.

Mucous membranes line internal body cavities exposed to the external environment, secreting mucus to trap foreign microbes.

Physical and mucosal barriers represent the body's primary non-specific line of defense.

2

Identify the primary internal non-specific cellular defense.

Phagocytes engulf and digest cellular debris and invading pathogens through phagocytosis.

Phagocytosis provides immediate, broad cellular defense without requiring specific antigen recognition.

3

Determine the role of humoral adaptive immune cells.

B lymphocytes produce specific antibodies tailored to neutralize extracellular pathogens and antigens.

Humoral immunity relies on B-cell activation and antibody secretion.

4

Determine the basis of acquired immunological memory.

Memory cells survive following an immune response to rapidly generate secondary defense upon reinfection.

Immunological memory provides long-lasting targeted protection against specific recurring pathogens.

Key Concept

Mechanisms and division of labor between innate surface barriers, innate cellular phagocytosis, and adaptive humoral immunity.

Estimated Time:1m 0s

Question 3062Question →

When a candle is lit, the heat from the flame causes the solid wax at the base of the wick to turn into liquid wax. Which of the following statements correctly describes this process?

It is a chemical change because heat breaks the wax molecules into completely new chemical substances.

It is a physical change because the wax changes its state of matter without altering its chemical composition.

It is a chemical change because the production of liquid from a solid indicates a chemical reaction occurred.

It is a physical change because the total mass of the wax decreases as it turns into a liquid.

Show answer & explanation

Answer: It is a physical change because the wax changes its state of matter without altering its chemical composition.

Answer

The melting of solid wax is a physical change because the wax changes its state of matter without altering its chemical composition.

Melting is a phase change from solid to liquid, which is a classic physical change. During melting, the physical state and molecular arrangement change, but no new chemical substances are formed and the chemical formula of the wax remains unchanged.

Step-by-Step Solution

1

Identify the process described in the scenario.

Solid wax changes into liquid wax due to heat, which is a phase change known as melting.

Determining the specific process allows classification as a physical or chemical event.

2

Analyze whether the chemical composition changes during melting.

The molecules of the wax remain identical before and after melting; only the distance and arrangement between particles change.

Physical changes involve changes in appearance or state without forming new chemical substances, whereas chemical changes produce new substances.

Key Concept

Physical versus chemical changes in matter

Estimated Time:45s

Question 3063Question →

When an oceanic plate collides with a continental plate at a convergent boundary, the oceanic plate is forced downward into the mantle. Why does the oceanic plate sink beneath the continental plate during this collision?

Continental crust is thinner and denser than oceanic crust, allowing it to displace the underlying oceanic slab.

Oceanic crust is denser and composed primarily of basaltic rock, causing it to sink beneath the less dense granitic continental crust.

Continental crust is older and cooler, creating downward thermal convection that pulls the oceanic plate into the mantle.

Oceanic crust contains a higher concentration of quartz and silica, which softens at lower temperatures to permit subduction.

Show answer & explanation

Answer: Oceanic crust is denser and composed primarily of basaltic rock, causing it to sink beneath the less dense granitic continental crust.

Answer

Oceanic crust is denser and composed primarily of basaltic rock, causing it to sink beneath the less dense granitic continental crust.

The correct answer identifies that subduction occurs because oceanic crust is denser than continental crust. Oceanic lithosphere is primarily mafic (basaltic) with a density of approximately

3.0\text{ g/cm}^3

, whereas continental lithosphere is primarily felsic (granitic) with a lower density of approximately

2.7\text{ g/cm}^3

. When compression occurs at a convergent boundary, the heavier oceanic lithosphere sinks into the semi-fluid asthenosphere beneath the more buoyant continental plate.

Step-by-Step Solution

1

Compare the composition and density of oceanic crust with continental crust.

Oceanic crust consists predominantly of basalt with a density of roughly

3.0\text{ g/cm}^3

, whereas continental crust consists predominantly of granite with a density of roughly

2.7\text{ g/cm}^3

.

Relative density governs the buoyancy and physical behavior of tectonic plates upon collision.

2

Apply the principles of isostasy and plate convergence to determine which plate subducts.

Because the basaltic oceanic plate is denser and heavier, gravitational slab pull forces it beneath the more buoyant granitic continental plate and down into the asthenosphere.

At a convergent boundary, the denser plate always subducts beneath the less dense plate.

Key Concept

Density-driven subduction at convergent plate boundaries

Estimated Time:1m 0s

Question 3064Question →

A remote-controlled toy boat with a mass of $2\text{ kg}$ accelerates across a calm pond at a rate of $3\text{ m/s}^2$ . What is the net horizontal force acting on the boat?

6\text{ kg}

6\text{ N}

1.5\text{ N}

6\text{ m/s}

Show answer & explanation

Answer: $6\text{ N}$

Answer

The net horizontal force acting on the boat is

6\text{ N}

.

Newton's second law of motion states that net force equals mass multiplied by acceleration (

F = ma

). Multiplying the mass of

2\text{ kg}

by the acceleration of

3\text{ m/s}^2

yields a net force of

6\text{ N}

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

Mass

m = 2\text{ kg}

and acceleration

a = 3\text{ m/s}^2

.

Determining the known variables allows the direct application of Newton's second law of motion.

2

Apply the formula for Newton's second law of motion (

F = ma

).

F = 2\text{ kg} \times 3\text{ m/s}^2 = 6\text{ N}

.

Multiplying mass in kilograms by acceleration in meters per second squared yields force in newtons (

1\text{ N} = 1\text{ kg}\cdot\text{m/s}^2

).

Key Concept

Newton's Second Law of Motion (

F = ma

)

Estimated Time:45s

Question 3065Question →

A science teacher simultaneously drops a steel hammer and a bird feather from the same height inside a sealed vacuum chamber that contains no air. Which of the following best predicts the motion of the two objects?

The hammer will hit the bottom first because an object with greater mass experiences a larger downward acceleration.

Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

The feather will hit the bottom first because an object with less mass attains downward velocity more quickly in a vacuum.

The hammer will hit the bottom first because its weight measured in metric units causes it to reach terminal velocity sooner.

Show answer & explanation

Answer: Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

Answer

Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

In the absence of air resistance, the only force acting on falling objects is gravity. Although a heavier object experiences a greater gravitational pull (weight), it also has proportionally greater inertia (resistance to acceleration). As a result of

a = \frac{F}{m} = g

, all objects accelerate downward at the constant rate of approximately

9.8\text{ m/s}^2

on Earth, reaching the surface at the exact same time when released together from the same height.

Step-by-Step Solution

1

Identify the external forces acting on the objects inside the chamber.

Only the downward force of gravity acts on the objects, as air resistance is zero in a vacuum.

Recognizing the environmental conditions determines whether drag forces affect the fall.

2

Apply Newton's second law of motion (

F = ma

) to determine acceleration due to gravity.

The acceleration is calculated as

a = \frac{F_g}{m} = \frac{mg}{m} = g

.

Demonstrates that the mass

m

cancels out, proving acceleration is independent of mass.

3

Compare the arrival times of both falling objects released from the same height.

Since both start from rest with identical acceleration

g

, both take time

t = \sqrt{\frac{2h}{g}}

to reach the bottom.

Confirms that both items strike the floor simultaneously.

Key Concept

Acceleration due to gravity in free fall without air resistance

Estimated Time:45s

Question 3066Question →

Deep-space navigation systems record the separation between our solar system and the Alpha Centauri star system as $4.37$ light-years. Which statement correctly identifies what this unit of measurement describes?

The duration of

4.37

years required for an exoplanet to complete one full orbit around its host star

The velocity at which electromagnetic signals propagate through interstellar vacuum

The physical span traversed by radiation in

4.37

standard Earth years

The estimated remaining lifespan of a stellar core before entering the red giant phase

Show answer & explanation

Answer: The physical span traversed by radiation in $4.37$ standard Earth years

Answer

The physical span traversed by radiation in

4.37

standard Earth years

In astronomy, a light-year is defined as the distance that electromagnetic radiation (light) travels through a vacuum in one Julian year. Therefore, a separation of

4.37

light-years indicates the total physical length traversed by light over

4.37

Earth years.

Step-by-Step Solution

1

Identify the physical dimension defined by the astronomical unit 'light-year'

A light-year is a unit of length (distance), not a measure of time or speed.

Because distances between stars are vast, astronomers quantify space intervals using the distance light travels in one Earth year (

~9.46 \times 10^{12}\text{ km}

).

2

Apply the definition to a value of

4.37

light-years

The value represents the distance covered by electromagnetic waves traveling at speed

c

over an interval of

4.37

years.

Multiplying the constant speed of light by the specified number of years yields the physical distance separating the two star systems.

Key Concept

Definition of the light-year as an astronomical unit of distance

Estimated Time:1m 0s

Question 3067Question →

In a coniferous forest food chain, bark beetles feed on pine wood, woodpeckers eat the bark beetles, and Cooper's hawks prey on the woodpeckers. Which organism functions as the secondary consumer?

Bark beetle

Woodpecker

Cooper's hawk

Pine tree

Show answer & explanation

Answer: Woodpecker

Answer

Woodpecker

In this food chain, the pine tree is the primary producer, the bark beetle is the primary consumer, the woodpecker is the secondary consumer because it feeds on primary consumers, and the Cooper's hawk is the tertiary consumer.

Step-by-Step Solution

1

Identify the base producer and first feeding tier in the chain.

The pine tree is the autotrophic producer, and the bark beetle feeding directly on it is the primary consumer (herbivore).

Trophic hierarchies begin with primary producers followed by primary consumers.

2

Determine the organism that feeds upon the primary consumer.

The woodpecker preys on the bark beetle, classifying the woodpecker as the secondary consumer.

Secondary consumers are carnivores or omnivores that obtain energy by consuming primary consumers.

Key Concept

Trophic levels and consumer roles in ecological food chains

Estimated Time:45s

Question 3068Question →

A $15\text{ kg}$ sled slides across a smooth ice rink at a constant velocity of $4\text{ m/s}$ . What is the magnitude of the sled's momentum in kilogram-meters per second ( $\text{kg}\cdot\text{m/s}$ )?

Show answer & explanation

Answer: 60

Answer

60 kg·m/s

Linear momentum is calculated using the formula

p = m \times v

. For an object with a mass of

15\text{ kg}

moving at

4\text{ m/s}

, the momentum is

15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

.

Step-by-Step Solution

1

Identify the given mass and velocity values.

m = 15\text{ kg}

and

v = 4\text{ m/s}

Linear momentum depends directly on an object's mass and its velocity.

2

Apply the momentum formula

p = m \times v

.

p = 15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

Multiplying mass by velocity calculates the magnitude of linear momentum.

Key Concept

Linear momentum is the product of an object's mass and its velocity (

p = mv

).

Estimated Time:45s

Question 3069Question →

An astronaut takes a $100 \text{ g}$ solid block of a pure substance, which has an initial volume of $20 \text{ cm}^3$ , to a planet with twice the gravity of Earth. On the new planet, the block is heated until it completely melts, expanding to a volume of $25 \text{ cm}^3$ . Which of the following accurately describes the substance on the new planet compared to its initial state on Earth?

Its mass remains

100 \text{ g}

, its weight is doubled, and it undergoes a physical change that decreases its density to

4.0 \text{ g/cm}^3

.

Its mass and weight both double, and it undergoes a physical change that results in a density of

8.0 \text{ g/cm}^3

.

Its mass remains

100 \text{ g}

, its weight is doubled, and it undergoes a chemical change that decreases its density to

4.0 \text{ g/cm}^3

.

Its mass and weight both double, and it undergoes a chemical change that results in a density of

8.0 \text{ g/cm}^3

.

Show answer & explanation

Answer: Its mass remains $100 \text{ g}$ , its weight is doubled, and it undergoes a physical change that decreases its density to $4.0 \text{ g/cm}^3$ .

Answer

The correct answer is that its mass remains 100 g, its weight is doubled, and it undergoes a physical change that decreases its density to 4.0 g/cm³.

The mass of an object is constant regardless of the gravitational environment, so it remains

100 \text{ g}

. Weight is a force dependent on gravity (

W = mg

), so placing the object in an environment with twice the gravity doubles its weight. Melting is a phase change, which is strictly a physical change, not a chemical one. Finally, density is mass divided by volume (

D = m/V

); since the mass is

100 \text{ g}

and the new volume is

25 \text{ cm}^3

, the resulting density is

4.0 \text{ g/cm}^3

.

Step-by-Step Solution

1

Determine the effect of increased gravity on mass and weight.

Mass remains

100 \text{ g}

, while weight doubles.

Mass is an intrinsic measure of the amount of matter and is independent of gravity, whereas weight is the gravitational force acting on that mass (

W = mg

).

2

Identify the type of change occurring during the melting process.

Melting is classified as a physical change.

A phase change from solid to liquid alters the state and volume of a substance but does not change its fundamental chemical composition.

3

Calculate the final density of the liquid on the new planet.

Density

= 4.0 \text{ g/cm}^3

.

Density is calculated as mass divided by volume. Using the constant mass (

100 \text{ g}

) and the new volume (

25 \text{ cm}^3

), the new density is

100 \text{ g} / 25 \text{ cm}^3 = 4.0 \text{ g/cm}^3

.

Key Concept

Distinguishing between mass and weight, classifying phase changes, and calculating density.

Estimated Time:2m 0s

Question 3070Question →

A rectangular glass container with internal base dimensions of $5\text{ cm}$ by $4\text{ cm}$ contains water. A solid mineral specimen with a mass of $130\text{ g}$ is completely submerged into the water, causing the water level to rise by $2.5\text{ cm}$ without spilling. What is the density of the mineral specimen in $\text{g/cm}^3$ ?

Show answer & explanation

Answer: 2.6

Answer

The density of the mineral specimen is

2.6\text{ g/cm}^3

.

Density is calculated by dividing mass by volume (

\rho = \frac{m}{V}

). The water displacement method reveals the object's volume:

\text{Volume} = \text{length} \times \text{width} \times \Delta h = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

. Dividing the given mass of

130\text{ g}

by the displaced volume of

50\text{ cm}^3

yields exactly

2.6\text{ g/cm}^3

.

Step-by-Step Solution

1

Calculate the volume of the displaced water inside the rectangular container.

V = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

The volume of fluid pushed upward corresponds to the area of the base multiplied by the change in water height.

2

Equate the volume of the submerged solid to the displaced fluid volume.

V_{\text{specimen}} = 50\text{ cm}^3

By the principle of fluid displacement, a completely submerged solid displaces a volume of fluid exactly equal to its own physical volume.

3

Calculate the density of the specimen using the mass-to-volume ratio.

\rho = \frac{m}{V} = \frac{130\text{ g}}{50\text{ cm}^3} = 2.6\text{ g/cm}^3

Density is an intensive physical property defined as mass per unit volume.

Key Concept

Density is an intensive physical property of matter defined as mass per unit volume (

\rho = m/V

), determinable for irregular or submerged solids via fluid displacement.

Estimated Time:1m 30s

Question 3071Question →

In mechanical systems, energy is transferred and transformed through various types of forces and work. Match each mechanical operation with its primary energy transformation or work process.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Compressing a suspension spring matches with conversion of mechanical work into elastic potential energy; applying friction brake pads matches with conversion of kinetic energy into thermal energy via frictional work; lifting an engine block vertically matches with conversion of mechanical work into gravitational potential energy; spinning up a flywheel from rest matches with conversion of mechanical work into rotational kinetic energy.

Each mechanical operation corresponds directly to a fundamental energy transition: deforming a spring stores elastic potential energy, friction converts moving kinetic energy into dissipated thermal energy, elevating a mass increases gravitational potential energy, and accelerating a rotating mass stores kinetic energy.

Step-by-Step Solution

1

Analyze the suspension spring compression

Work is done against spring tension, resulting in stored elastic potential energy.

Deforming an elastic medium stores mechanical energy internally.

2

Analyze the friction braking process

Kinetic energy of motion is converted directly into heat through friction.

Friction opposes motion over a distance, converting mechanical energy into thermal energy.

3

Analyze the vertical lifting hoist

Work done against Earth's gravitational pull increases gravitational potential energy (

PE = mgh

).

Increasing height at constant speed transfers work directly into gravitational potential energy.

4

Analyze the accelerating flywheel

Work applied as torque increases the angular velocity and rotational kinetic energy (

KE = \frac{1}{2}I\omega^2

).

Accelerating mass into motion represents an accumulation of kinetic energy.

Key Concept

Work-Energy Theorem and Forms of Energy Transformation

Estimated Time:1m 0s

Question 3072Question →

In physical oceanography, the open ocean water column is divided into distinct pelagic zones based on depth and solar radiation penetration. Match each oceanic depth zone with its defining environmental and light characteristics. How do these vertical marine zones correctly correspond to their depth and illumination profiles?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Epipelagic Zone matches the sunlit surface layer (0–200 m) where photosynthesis occurs; Mesopelagic Zone matches the twilight layer (200–1,000 m) with faint light insufficient for photosynthesis; Bathypelagic Zone matches the midnight layer (1,000–4,000 m) of complete darkness and high pressure; and Hadalpelagic Zone matches the deepest marine layer (below 6,000 m) in ocean trenches.

The correct pairings accurately reflect vertical pelagic stratification: the Epipelagic zone is the photic layer (0–200 m) capable of supporting photosynthesis; the Mesopelagic zone is the dysphotic twilight layer (200–1,000 m); the Bathypelagic zone represents the aphotic midnight layer (1,000–4,000 m); and the Hadalpelagic zone encompasses the extreme depths of ocean trenches below 6,000 m.

Step-by-Step Solution

1

Identify the shallowest, fully illuminated layer of the water column.

The Epipelagic Zone extends from the surface to roughly 200 meters and is the photic zone where sunlight sustains photosynthesis.

Phytoplankton require solar irradiance, which is restricted to the upper 200 meters of the water column.

2

Distinguish the intermediate zone where light is detectable but biologically limiting for autotrophs.

The Mesopelagic Zone spans from 200 to 1,000 meters and is termed the twilight zone due to minimal light penetration.

Light rapidly attenuates with depth in seawater, dropping below photosynthetic compensation levels by 200 meters.

3

Identify the aphotic deep-water layer extending to 4,000 meters.

The Bathypelagic Zone spans 1,000 to 4,000 meters, characterized by complete darkness, near-freezing temperatures, and high pressure.

All visible solar radiation is fully absorbed by 1,000 meters depth in open ocean waters.

4

Classify the deepest benthic and pelagic zones occurring below 6,000 meters.

The Hadalpelagic Zone designates deep ocean trench environments reaching depths beyond 6,000 meters down to the ocean floor.

The term 'hadal' refers to the deepest oceanic trenches formed along tectonic subduction zones.

Key Concept

Vertical zonation of the pelagic ocean based on depth, hydrostatic pressure, and light penetration

Estimated Time:1m 0s

Question 3073Question →

The human digestive system relies on coordinated specialized organs to chemically break down food, absorb essential nutrients, and maintain metabolic homeostasis. Match each digestive organ on the left with its primary physiological function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Stomach matches with secreting hydrochloric acid and pepsinogen for protein digestion; Liver matches with producing bile to emulsify lipids; Pancreas matches with secreting digestive enzymes and neutralizing bicarbonate; Small intestine matches with serving as the primary site for nutrient absorption across mucosal villi.

Each organ is correctly aligned with its physiological function: the stomach initiates protein digestion via gastric acid and pepsin; the liver produces bile to emulsify fats; the pancreas provides vital digestive enzymes and bicarbonate buffer; and the small intestine provides the extensive epithelial surface area needed for nutrient monomer absorption.

Step-by-Step Solution

1

Identify the primary chemical and mechanical role of the stomach in digestion.

The stomach is characterized by gastric acid (hydrochloric acid) and pepsinogen secretion for protein breakdown.

Gastric glands specifically produce these secretions to begin chemical digestion of proteins in a low pH environment.

2

Determine the non-enzymatic digestive contribution of the liver.

The liver produces bile salts necessary for lipid emulsification.

Bile increases the surface area of dietary fats so water-soluble lipases can digest them effectively.

3

Analyze the dual exocrine secretion of the pancreas into the alimentary canal.

The pancreas delivers digestive enzymes for all macronutrient classes and bicarbonate to buffer acidity.

Pancreatic enzymes require a near-neutral to slightly basic pH to function optimally in the duodenum.

4

Identify the primary site of systemic nutrient absorption.

The small intestine completes digestion and absorbs the resulting nutrient monomers.

The microvillar brush border of the small intestinal epithelium provides the surface area required for nutrient uptake.

Key Concept

Specialized physiological roles of primary and accessory human digestive organs in nutrient breakdown and absorption.

Estimated Time:1m 0s

Question 3074Question →

In physical science, chemical reactions are categorized by how reactant atoms and compounds interact to form products. Match each described chemical reaction scenario on the left with its correct reaction classification on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Burning propane in oxygen matches Combustion; Splitting water into hydrogen and oxygen matches Decomposition; Combining magnesium and oxygen into magnesium oxide matches Synthesis; Mixing hydrochloric acid and sodium hydroxide matches Neutralization.

Each process demonstrates a core category of chemical change: burning propane with oxygen to produce carbon dioxide and water is combustion; splitting water into hydrogen and oxygen gas via electricity is decomposition; combining magnesium and oxygen into a single compound is synthesis; and mixing hydrochloric acid with sodium hydroxide to create salt and water is neutralization.

Step-by-Step Solution

1

Identify the reaction where a fuel rapidly reacts with oxygen gas (

O_2

) producing energy, carbon dioxide (

CO_2

), and water (

H_2O

).

Burning propane corresponds to a Combustion reaction (

C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O

).

Combustion occurs when a substance combines with oxygen rapidly, releasing heat and light.

2

Identify the process where a single reactant compound breaks down into two or more distinct products.

Splitting water into hydrogen and oxygen corresponds to a Decomposition reaction (

2H_2O \rightarrow 2H_2 + O_2

).

Decomposition represents the breakdown of a single substance into simpler parts.

3

Identify the process where two or more individual reactants join together to create a single compound.

Combining magnesium and oxygen into magnesium oxide corresponds to a Synthesis reaction (

2Mg + O_2 \rightarrow 2MgO

).

Synthesis involves building up a larger or more complex molecule from simpler elements or compounds.

4

Identify the reaction where an acidic solution and a basic solution react to yield a neutral salt and water.

Mixing hydrochloric acid and sodium hydroxide corresponds to a Neutralization reaction (

HCl + NaOH \rightarrow NaCl + H_2O

).

Neutralization is an acid-base double displacement reaction where hydrogen and hydroxide ions combine to form water.

Key Concept

Classifying Fundamental Chemical Reactions

Estimated Time:45s

Question 3075Question →

In residential heating, propane gas ( $\text{C}_3\text{H}_8$ ) burns in the presence of oxygen ( $\text{O}_2$ ) to form carbon dioxide ( $\text{CO}_2$ ) and water vapor ( $\text{H}_2\text{O}$ ) according to the unbalanced chemical equation:

\text{C}_3\text{H}_8 + \underline{\hspace{0.8cm}}\,\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O}

What coefficient must be placed before $\text{O}_2$ to completely balance this equation using the lowest whole numbers?

10

5

7

3

Show answer & explanation

Answer: 5

Answer

5

The coefficient 5 is correct because the product side contains a total of 10 oxygen atoms (6 from

3\text{CO}_2

and 4 from

4\text{H}_2\text{O}

). Since molecular oxygen is diatomic (

\text{O}_2

), 5 molecules of

\text{O}_2

(

5 \times 2 = 10

atoms) are required to balance the reaction.

Step-by-Step Solution

1

Count the total number of oxygen atoms on the product side of the equation.

The products contain

(3 \times 2) + (4 \times 1) = 6 + 4 = 10

oxygen atoms.

By the Law of Conservation of Mass, the number of oxygen atoms in the reactants must equal the number in the products.

2

Determine the coefficient needed for diatomic oxygen gas (

\text{O}_2

) on the reactant side.

10 \div 2 = 5

Because each

\text{O}_2

molecule contains 2 oxygen atoms, 5 molecules are required to provide the 10 needed atoms.

Key Concept

Balancing chemical equations by conserving atoms across reactants and products

Estimated Time:1m 0s

Question 3076Question →

In a submarine life-support system, carbon dioxide ( $CO_2$ ) is scrubbed from the cabin atmosphere by reacting with solid lithium hydroxide ( $LiOH$ ) to produce solid lithium carbonate ( $Li_2CO_3$ ) and water vapor ( $H_2O$ ). Which of the following represents the correctly balanced chemical equation for this reaction?

LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Li_2OH + CO_2 \rightarrow Li_2CO_3 + H_2O

LiOH + CO_2 \rightarrow LiCO_2 + H_2O

Show answer & explanation

Answer: $2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O$

Answer

The balanced chemical equation is

2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

.

Placing a coefficient of 2 in front of lithium hydroxide yields equal quantities of each element on both sides: 2 lithium atoms, 1 carbon atom, 4 oxygen atoms, and 2 hydrogen atoms, satisfying the law of conservation of mass.

Step-by-Step Solution

1

Write the unbalanced skeleton equation using the correct chemical formulas for all reactants and products.

LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Establishing the correct formulas ensures that the identities of the chemical substances are maintained.

2

Count the number of each type of atom on both sides of the equation.

Reactants: 1 Li, 1 C, 3 O, 1 H. Products: 2 Li, 1 C, 4 O, 2 H.

An atom inventory reveals which elements violate the law of conservation of mass.

3

Place a coefficient of 2 in front of

LiOH

on the reactant side to balance the lithium and hydrogen atoms.

2LiOH + CO_2 \rightarrow Li_2CO_3 + H_2O

Using whole-number coefficients balances atoms without altering compound identities.

4

Re-verify the atom count for every element across the entire equation.

Reactants: 2 Li, 1 C, 4 O, 2 H. Products: 2 Li, 1 C, 4 O, 2 H.

Confirming equal atom counts ensures the equation satisfies the law of conservation of mass.

Key Concept

Balancing chemical equations by adding stoichiometric coefficients while keeping chemical formulas unchanged.

Estimated Time:1m 30s

Question 3077Question →

Throughout its existence, a low- to medium-mass star like the Sun undergoes a series of predictable structural and nuclear transformations. Place the following stages of a Sun-like star's evolutionary life cycle in chronological order from earliest to latest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Stellar nebula condensing into a protostar → Main sequence star fusing hydrogen → Red giant expansion → Planetary nebula shedding outer layers → White dwarf cooling core remnant

The chronological sequence begins with gravitational collapse within a stellar nebula to form a protostar. Once core hydrogen fusion begins, the star spends most of its life on the main sequence. After core hydrogen is depleted, it expands into a red giant. The pulsating outer layers are subsequently cast off as an expanding planetary nebula, leaving behind only the hot, dense core as a cooling white dwarf.

Step-by-Step Solution

1

Identify the star formation stage

Stellar nebula condensing and collapsing into a protostar

Stars originate from giant clouds of gas and dust (nebulae) that collapse under gravity.

2

Identify the stable equilibrium stage

Main sequence star fusing hydrogen into helium in its core

When core temperatures reach the threshold for hydrogen fusion, the star enters its primary, stable lifespan.

3

Identify the post-main-sequence expansion stage

Red giant expanding after core hydrogen depletion

Depletion of core hydrogen disrupts hydrostatic equilibrium, causing core contraction and massive expansion of the outer layers.

4

Identify the envelope ejection stage

Planetary nebula shedding outer gas layers into space

For low- to medium-mass stars, thermal pulsations gently expel the outer gaseous envelope rather than detonating as a supernova.

5

Identify the final remnant stage

White dwarf cooling as a dense, hot carbon-oxygen core remnant

The inactive, degenerate core remains behind as a white dwarf, which gradually cools over cosmic timescales.

Key Concept

Evolutionary life cycle sequence of low-to-medium mass (Sun-like) stars

Estimated Time:1m 0s

Question 3078Question →

When the left ventricle of the human heart contracts, it propels oxygen-rich blood under high pressure directly into which major blood vessel to initiate systemic circulation throughout the body?

Superior vena cava

Inferior vena cava

Aorta

Hepatic portal vein

Show answer & explanation

Answer: Aorta

Answer

The aorta is the major artery that receives oxygenated blood from the left ventricle to supply the entire systemic circuit.

During ventricular systole, the left ventricle generates high pressure to force oxygen-rich blood through the aortic valve into the aorta, which serves as the main trunk of the systemic arterial system.

Step-by-Step Solution

1

Identify the chamber of the heart specified and its role in circulation.

The left ventricle pumps newly oxygenated blood out of the heart into the high-pressure systemic circuit.

The left side of the heart is dedicated to systemic circulation, moving oxygen-rich blood to peripheral tissues.

2

Determine the anatomical vessel directly connected to the left ventricle.

The aorta connects directly to the left ventricle across the aortic semilunar valve.

The aorta is the primary conduit that branches into systemic arteries distributing oxygenated blood throughout the body.

Key Concept

Cardiovascular systemic arterial outflow and ventricular ejection

Estimated Time:45s

Question 3079Question →

A pneumatic test probe is launched vertically upward from ground level with an initial kinetic energy of $450\text{ J}$ . Assuming air resistance is negligible, what is the kinetic energy of the probe at the point where it has gained $300\text{ J}$ of gravitational potential energy?

300\text{ J}

150\text{ J}

750\text{ J}

0\text{ J}

Show answer & explanation

Answer: $150\text{ J}$

Answer

150\text{ J}

In the absence of air resistance, the total mechanical energy of the system remains constant (

E = KE + PE = 450\text{ J}

). When the probe gains

300\text{ J}

of gravitational potential energy, the remaining kinetic energy is

450\text{ J} - 300\text{ J} = 150\text{ J}

.

Step-by-Step Solution

1

Determine the total initial mechanical energy of the probe at launch.

Total Mechanical Energy (

E

) =

450\text{ J}

At ground level before rising, all mechanical energy is kinetic energy (

KE = 450\text{ J}

,

PE = 0\text{ J}

).

2

Apply the law of conservation of mechanical energy.

E = KE + PE = 450\text{ J}

In the absence of air resistance, the total mechanical energy of the system remains constant throughout the upward climb.

3

Calculate the remaining kinetic energy at the given potential energy level.

KE = 450\text{ J} - 300\text{ J} = 150\text{ J}

Subtract the gained gravitational potential energy from the total conserved mechanical energy.

Key Concept

Conservation of Mechanical Energy

Estimated Time:1m 0s

Question 3080Question →

A sealed, rigid $250\text{ mL}$ container holds $50\text{ g}$ of solid carbon dioxide (dry ice) at sea level on Earth. The container is transported to a research outpost on Mars, where surface gravity is approximately $38\%$ of Earth's gravity. During transport, the dry ice completely sublimates into carbon dioxide gas at room temperature inside the sealed container. Which statement correctly evaluates the physical and chemical properties of the carbon dioxide upon arrival at Mars?

Sublimation is a chemical change that forms a new gas compound, reducing the total mass of the sealed system while its weight remains constant.

Sublimation is a physical change that conserves the

50\text{ g}

mass of carbon dioxide, while the weight of the substance decreases due to lower Martian gravity.

Sublimation is a physical change, but the mass of the carbon dioxide decreases to

38\%

of its Earth value because of the reduced gravitational field.

Sublimation is a chemical change where intramolecular bonds break into individual elements, causing both the mass and weight of the carbon dioxide to decrease.

Show answer & explanation

Answer: Sublimation is a physical change that conserves the $50\text{ g}$ mass of carbon dioxide, while the weight of the substance decreases due to lower Martian gravity.

Answer

Sublimation is a physical change that conserves the

50\text{ g}

mass of carbon dioxide, while the weight of the substance decreases due to lower Martian gravity.

The correct answer accurately states that sublimation (transition from solid directly to gas) is a physical change preserving the chemical identity of

CO_2

. Because the container is sealed, the mass remains invariant at

50\text{ g}

. However, because Martian gravity is only

38\%

of Earth's gravity, the weight (

W = mg

) decreases accordingly.

Step-by-Step Solution

1

Classify the phase change process (sublimation).

Sublimation is a physical change, not a chemical change.

Converting solid carbon dioxide to gaseous carbon dioxide changes only the physical state and arrangement of molecules, not their chemical composition.

2

Determine the mass of the substance in the sealed container on Mars.

Mass remains exactly

50\text{ g}

.

According to the Law of Conservation of Mass, matter is neither created nor destroyed in a closed system, and mass is an intrinsic property independent of gravity.

3

Analyze the effect of Martian gravity on the weight of the substance.

Weight decreases to approximately

38\%

of its Earth value.

Weight is the gravitational force exerted on an object (

W = mg

), which is directly proportional to the local gravitational field strength.

Key Concept

Distinction between physical vs. chemical changes and mass vs. weight across varying gravitational environments

Estimated Time:1m 30s

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