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All questions of Thermochemistry & Thermodynamics (GC, PHY) for MCAT Exam

Additional gas is pumped inside a rigid container that stores compressed gas. Which of the following is a true statement about this system?
  • a)
    Pressure is constant throughout the compression.
  • b)
    There is no work done on the container.
  • c)
    The molar concentration of gas is decreasing.
  • d)
    The volume of the container is decreasing.
Correct answer is option 'B'. Can you explain this answer?

Samuel Lewis answered
Explanation:
When additional gas is pumped inside a rigid container that stores compressed gas, several changes occur in the system. Let's analyze each statement to determine which one is true.

a) Pressure is constant throughout the compression:
This statement is not true. When additional gas is pumped into the container, the volume of the container remains constant while the number of gas molecules increases. According to the ideal gas law (PV = nRT), if the volume (V) is constant and the number of moles (n) increases, then the pressure (P) must also increase. Therefore, the pressure is not constant throughout the compression.

b) There is no work done on the container:
This statement is true. Since the container is rigid, there is no change in volume, and work is defined as the product of force and displacement. Without a change in volume, there is no displacement, and therefore no work is done on the container.

c) The molar concentration of gas is decreasing:
This statement is not true. When additional gas is pumped into the container, the number of gas molecules increases, while the volume remains constant. As a result, the molar concentration of the gas, which is defined as the number of moles of gas divided by the volume, will increase rather than decrease.

d) The volume of the container is decreasing:
This statement is not true. The problem states that additional gas is pumped into the container, which implies that the volume of the container is not decreasing. In a rigid container, the volume remains constant regardless of the changes in the amount of gas inside.

Therefore, the correct statement is option 'B' - There is no work done on the container.

Which of the following scenarios violates the first law of thermodynamics, “the conservation of energy?"
  • a)
    A spring that extends and retracts forever, alternating between potential and kinetic energy.
  • b)
    An isolated electrochemical cell that indefinitely generates an electrical current.
  • c)
    An efficient wind turbine that converts all of its energy from mechanical movement into electrical potential energy.
  • d)
    A machine that converts heat energy into work energy.
Correct answer is option 'B'. Can you explain this answer?

Emma Smith answered
The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. Therefore, any scenario that involves the creation or destruction of energy would violate the first law of thermodynamics.

1. A car engine converts chemical energy from gasoline into thermal energy and mechanical energy to move the car. This does not violate the first law of thermodynamics as energy is being converted from one form to another.
2. A refrigerator uses electrical energy to transfer heat from inside the refrigerator to the outside, cooling the contents inside. This also does not violate the first law of thermodynamics as energy is being transferred from one location to another.
3. A perpetual motion machine that creates energy out of nothing and can operate indefinitely without an external energy source. This scenario violates the first law of thermodynamics as it involves the creation of energy from nothing, which is not possible according to the law.
4. A power plant that produces electricity by burning fossil fuels and releases waste heat into the environment. This does not violate the first law of thermodynamics as energy is being converted from chemical energy in the fuel to electrical energy, and the waste heat is transferred to the environment.
5. A solar panel that converts sunlight into electrical energy. This also does not violate the first law of thermodynamics as energy is being converted from solar radiation to electrical energy.

Which of the following reactions is most likely to be spontaneous only at high temperatures?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Ayesha Joshi answered
We are looking for a negative value of ∆Gto ascertain spontaneity. However, the condition of high temperatures would preclude some options.
When the sign for ∆H and ∆S are different, the system is either always spontaneous or non-spontaneous. When the signs are the same, there is the temperature-dependent spontaneity.
Only when both sign are positive is ∆G spontaneous at high temperatures. We are looking for an endothermic reaction with a positive entropy.
Evaluating the change in entropy should allow us to more easily eliminate. The formation of ammonia and nitrogen dioxide both show a negative change in entropy, whereby moles of gases are reduced on the product side.
Of the remaining two reactions, one is a combustion reaction, which is strongly exothermic, and can be eliminated.
The decomposition of dinitrogen tetraoxide shows an increase in entropy.

What is the net work done on the gas as it goes from point C to D and then to E on the Pressure vs Volume diagram?
  • a)
    0 J
  • b)
    -500 J
  • c)
    500 J
  • d)
    1000 J
Correct answer is option 'C'. Can you explain this answer?

Ayesha Joshi answered
We can calculate work as the area under the line graph in the diagram.
The volume of the gas is decreased, so the value of work done on the gas is positive.
The magnitude of work will be the area under the function from C to D. The path from D to E is vertical, so there is no work being done during this portion.
250 Pa x 2 m3 = 500 J.
And 500 J + 0J = 500 J.

What is the net work done on the gas as it goes from point A to B on the Pressure vs Volume diagram?
  • a)
    200 J
  • b)
    0 J
  • c)
    -200 J
  • d)
    100 J
Correct answer is option 'C'. Can you explain this answer?

Orion Classes answered
Since the gas is kept at a constant pressure, we can calculate work with W = PΔV.
The volume of the gas is increased so the value of work done on the gas is negative.
The magnitude of work will be the area of under the function from A to B. Which is 200 in the case. The net work done on the gas as it goes from point A to B is −200 J.

The standard enthalpy of formation (ΔHf°) of an element in its most stable form is:
  • a)
    Always positive
  • b)
    Always negative
  • c)
    Zero
  • d)
    Variable depending on the element
Correct answer is option 'C'. Can you explain this answer?

Ayesha Joshi answered
The standard enthalpy of formation (ΔHf°) of an element in its most stable form is defined as zero. This is because the formation of an element from its constituent elements does not involve any net energy change.

Equal amounts of heat are absorbed by 100 g, samples of various solid metals with differing specific heat values. Which of the following statements is true regarding metals and their specific heat values?
  • a)
    The metal with the smallest specific heat will undergo the smallest change in temperature.
  • b)
    The metal with the smallest specific heat will resist melting to a greater degree at its melting point.
  • c)
    The metal with the greatest specific heat will undergo the smallest change in temperature.
  • d)
    The metal with the greatest specific heat will resist melting to a greater degree at its melting point.
Correct answer is option 'C'. Can you explain this answer?

Ayesha Joshi answered
The specific heat capacity refers to the amount of heat required to cause a unit of mass to change its temperature by 1°C.
The specific heat capacity does not refer to a material’s resistance to melting at its melting point. This is value is referred to as the heat of fusion, ΔHfusion​
The specific heat capacity is a proportion that affects how a material’s absorption or release of heat changes its temperature. It is detailed by the equation: q = mcΔT, where q is heat, c is the specific heat capacity, and ΔT is the change in temperature.
According to the q = mcΔT equation, as long as the provided masses of metal solids are the same, the metal with the greatest specific heat will undergo the smallest change in temperature for a given heat energy value.

Atmospheric gases absorb more energy than they emit. If we consider a gas to be a closed system, which of the following is true?
  • a)
    The heat absorbed by the gas is positive.
  • b)
    The internal energy of the gas increases.
  • c)
    The change in volume of the gas is negative.
  • d)
    The work done on the gas is equal to the change in internal energy and the heat absorbed by the gas.
Correct answer is option 'A'. Can you explain this answer?

Answer:

To understand why option 'A' is the correct answer, let's break down the given information and analyze it step by step.

1. Atmospheric gases absorb more energy than they emit:
This statement implies that the gas is gaining more energy from its surroundings than it is losing. In other words, the net transfer of energy is from the surroundings to the gas. This indicates that the gas is gaining heat from its surroundings.

2. Considering the gas as a closed system:
In a closed system, energy can be exchanged between the system and its surroundings, but no matter is exchanged. In this case, the gas is the system under consideration, and its surroundings provide the energy in the form of heat.

3. Heat absorbed by the gas is positive:
Since the gas is absorbing more energy than it emits, the heat absorbed by the gas is positive. This means that the energy transferred to the gas from its surroundings is greater than the energy lost by the gas. Therefore, option 'A' is the correct answer.

4. Internal energy of the gas:
The internal energy of a closed system is the sum of its kinetic and potential energies. Since the gas is gaining energy from its surroundings, the internal energy of the gas will increase.

5. Change in volume of the gas:
The given information does not provide any indication of the change in volume of the gas. Therefore, we cannot conclude whether the change in volume of the gas is negative or positive based on the given information.

6. Work done on the gas:
The given information does not provide any indication of the work done on the gas. Therefore, we cannot conclude whether the work done on the gas is equal to the change in internal energy and the heat absorbed by the gas based on the given information.

In conclusion, based on the information provided, option 'A' is the correct answer because atmospheric gases absorb more energy than they emit, and therefore, the heat absorbed by the gas is positive.

Which of the following statements best characterizes the data represented in the liquid-vapor phase diagram of carbon dioxide where the dotted line represents phase change?
  • a)
    Point 5 is the critical point of carbon dioxide.
  • b)
    Moving from point 1 to 2, carbon dioxide is undergoing condensation.
  • c)
    Moving left along the isotherm from point 1, the pressure increases drastically since carbon dioxide becomes an incompressible solid.
  • d)
    Above the isotherm for 31C, carbon dioxide exists only as a supercritical fluid.
Correct answer is option 'D'. Can you explain this answer?

Ayesha Joshi answered
This is a P-V graph, so the plotted lines represent isotherms, whereby each line represents a different temperature. Normally, the plot is hyperbolic in shape, but as the temperature decreases, the plot flattens into a liquid-vapor equilibrium region or condensation region.
Moving from point 1 to 2, carbon dioxide is undergoing evaporation not condensation since the liquid region is to the left and the vapor region is to the right.
To the left of point 1, the pressure increases drastically because carbon dioxide has condensed into an incompressible liquid not solid.
Point 3 is the critical point of carbon dioxide, and the isotherm through point 3 is the critical isotherm.
Above the isotherm through point 3, carbon dioxide exists only as a supercritical fluid.

In a system undergoing adiabatic compression, what are the values of internal energy and heat if work done on the system is 500 J?
  • a)
    Internal energy is 0 J and heat is 500 J.
  • b)
    Internal energy is -500 J and heat is 0 J.
  • c)
    Internal energy is 0 J and heat is -500 J.
  • d)
    Internal energy is 500 J and heat is 0 J.
Correct answer is option 'D'. Can you explain this answer?

Ayesha Joshi answered
This is an adiabatic process which means there is no heat transfer, q = 0.
According to the first law of thermodynamics, internal energy is equal to the sum of the heat within the system and the work done on the system. ΔU = q + w 
Following the first law of thermodynamics equation:

Which of the following statements can reasonably be deduced from the phase diagram of helium below?
  • a)
    At atmospheric pressure, helium can exist in all three phases, as well as a supercritical fluid phase near absolute zero.
  • b)
    Solid and gaseous helium never exist in equilibrium with each other at any temperature or pressure.
  • c)
    Helium does not exist as a solid below 25 atmospheres due to its low mass.
  • d)
    At room temperature, helium exists as a gas, and as pressure increases eventually becomes a solid.
Correct answer is option 'B'. Can you explain this answer?

Orion Classes answered
Helium has some peculiar features in its phase diagram. A typical phase diagram looks like the following:
At room temperature, helium exists as a gas, and as pressure increases it eventually becomes a liquid. Looking at the line boundary between solid and the two liquid phases, the line curves up. Since the graph is using the logarithmic scale, the line curves more steeply than it would seem.
At atmospheric pressure, helium can exist as a supercritical fluid (He-II), normal liquid (He-I), and gas, but not as a solid.
Helium does not exist as a solid below 25 atmospheres due to the weak London dispersion forces that exist between noble gas atoms.

Which of the following equations represents a formation reaction?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Ayesha Joshi answered
The standard enthalpy of formation of a compound is defined as the heat associated with the formation of one mole of the compound from its elements in their standard states. Most formation reactions are exothermic, but some are endothermic.
Carbon monoxide (CO) is not an element, in its reaction with oxygen gas, so the reaction is not a formation reaction.
In the reaction with hydrogen and bromine gases reacting, bromine is not in its standard state, which is liquid not gas. Bromine and mercury are the only two elements that are liquid in its standard state. The formation reaction of HBr would look like this:
H2 (g) + Br2 (1) + 2BHr (g)
In the reaction with hydrogen and oxygen gases reacting, water on the product state is not in its standard state. The formation reaction of H2O would look like this:
In the reaction with rhombic sulfur and chlorine gas, there are elements in their standard state on the reactant side and only one product in its standard state. Sulfur is peculiar in that sulfur is not monoatomic and additionally has two forms, rhombic and monoclinic, and rhombic is the more stable form. The formation reaction of is SC12 correct as stated.

Which of the following best defines enthalpy?
  • a)
    The measure of disorder in a system
  • b)
    The amount of heat released or absorbed in a chemical reaction
  • c)
    The energy required to break chemical bonds
  • d)
    The capacity to do work or transfer heat
Correct answer is option 'B'. Can you explain this answer?

Ayesha Joshi answered
An exothermic reaction is a chemical reaction that releases heat energy to the surroundings. It is characterized by a negative change in enthalpy, indicating a decrease in the energy content of the system.

Which of the following processes is associated with a positive entropy change?
  • a)
    Melting of ice
  • b)
    Dissolution of a gas in water
  • c)
    Combustion of a hydrocarbon
  • d)
    Condensation of a vapor
Correct answer is option 'B'. Can you explain this answer?

Ayesha Joshi answered
The dissolution of a gas in water is associated with a positive entropy change. When a gas dissolves, its particles become dispersed in the liquid, increasing the disorder or randomness of the system, which corresponds to an increase in entropy.

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