AP Chemistry - Laws of Thermodynamics

A chemistry student is trying to calculate how long it will take a power source of to heat a sample of ice from $-35^{o}C$ to $75^{o}C$ . Given that the specific heat capacity of ice is $2.06\frac{J}{g^{o}C}$ , the specific heat capacity of liquid water is $4.184\frac{J}{g^{o}C}$ , and the heat of fusion for water is $334.16\frac{J}{g}$ , how long will this process take?

There is not enough information to determine the amount of time needed for the process described

Explanation

In order to solve this problem, we'll need to break it up into steps.

Step 1: Calculate the amount of energy necessary to raise the sample of ice from $-35^{o}C$ to $0^{o}C$ . To do this, we'll need to use the following equation:

$q_{1}=mc_{H_{2}O(s)}\Delta T$

$q_{1}=( 20\cdot 10^{3}g)\left ( 2.06\frac{J}{g^{0}C} \right )\left ( 35^{o}C \right )=1.44\cdot 10^{6}J$

Step 2: Calculate the amount of energy necessary to convert the sample at $0^{o}C$ from ice to water. We'll need to make use of the following equation:

$q_{2}=m\Delta H_{fus(H_{2}O)}$

$q_{2}=\left ( 20\cdot 10^{3}g \right )\left ( 334.16\frac{J}{g} \right )=6.68\cdot 10^{6}J$

Step 3: Calculate the amount of energy necessary to convert the sample of water from $0^{o}C$ to $75^{o}C$ .

$q_{3}=mc_{H_{2}O(l)}\Delta T$

$q_{3}=\left ( 20\cdot 10^{3}g \right )\left ( 4.184\frac{J}{g^{o}C} \right )\left ( 75^{o}C \right )=6.28\cdot 10^{6}J$

Step 4: Sum the amount of energy from the previous 3 steps. This value is the total amount of energy for the entire process.

$q_{Total}=q_{1}+q_{2}+q_{3}=1.44\cdot 10^{7}J$

Step 5: Now that we know the total amount of energy needed for the process, we need to calculate the time based on the amount of power provided.

$P=\frac{q_{Total}}{t}$

$t=\frac{q_{Total}}{P}=\frac{\left ( 1.44\cdot 10^{7}J \right )}{(100\frac{J}{s}) }=1.44\cdot 10^{5}s$

$t=(1.44\cdot10^{5}s)\left ( \frac{1hr}{3600s} \right )=40hrs$

Which of the following is a law of thermodynamics?

ΔH (system) + ΔH (surroundings) = ΔH (universe)

ΔS (system) + ΔS (surroundings) = ΔS (universe)

ΔE (surroundings) = ΔE (system)

The entropy of the universe is always decreasing

Explanation

The second law of thermodynamics states that the entropy of the system and the entropy of the surroundings is equal to the entropy of the universe. The rest of the answer choices are not one of the fundamental laws of themodynamics.

Which of the following is true regarding the first law of thermodynamics?

It states that the heat lost by a system is gained by the surroundings

Conversion of kinetic energy to potential energy violates the first law of thermodynamics

It states that the disorder in the universe is always increasing

An exothermic reaction always destroys energy, whereas an endothermic reaction always creates energy

Explanation

First law of thermodynamics states that the energy of the universe is always constant. This is called the conservation of energy. The total energy of the universe is defined as follows:

According to the law, energy gained or lost by a system is reciprocated by its surroundings. This means that energy, such as heat energy, lost by the system will be gained by the surroundings. This will keep the total energy constant. Energy can be converted from one form to another (such as from kinetic to potential); however, it cannot be created or destroyed.

The second law of thermodynamics states that the disorder of the universe is always increasing. As mentioned, energy can never be created, nor destroyed. In an exothermic reaction, heat energy is transferred from the system to the surroundings. In an endothermic reaction, heat energy is transferred from the surroundings to the system.

Which of the following substances will have the lowest entropy?

Product of a freezing reaction

Product of a vaporization reaction

Liquid water

Water vapor

Explanation

Entropy is a measure of disorder; therefore, a substance with low entropy will be highly ordered. Gases have the highest entropy because the molecules are spread far apart and are more chaotic. Solids, on the other hand, have the least entropy because they are typically found in an ordered, lattice structure with very little chaos. A freezing reaction involves conversion of a liquid to a solid; therefore, the product of this reaction will have the lowest entropy.

A researcher creates a perfect crystal and stores it at $-273.15^\circ C$ . What can you conclude about this substance?

I. The entropy of this substance is less than zero

II. It will have more microstates than gaseous nitrogen

III. Its Gibbs free energy is equal to its enthalpy

III only

I only

I and III

II and III

Explanation

The third law of thermodynamics states that a perfect crystal at absolute zero ( or $-273.15^\circ C$ ) has an entropy of zero (lowest possible entropy). Note that entropy can never be less than zero.

Microstates are microscopic configurations of a substance, and relates directly to the entropy of the system. The more microstates, the higher the entropy. Since this substance has the lowest entropy it will have the least amount of microstates.

To understand the relationship between Gibbs free energy and enthalpy, we need to look at the following equation:

$\Delta G = \Delta H - T\Delta S$

Here, $\Delta G$ is change in Gibbs free energy, $\Delta H$ is enthalpy, $\Delta S$ is change in entropy, and is the temperature in Kelvin. From the given information, we know that both temperature and entropy are zero; therefore, Gibbs free energy equals the enthalpy for this substance.

"In a natural thermodynamic process, the sum of the entropies of the interacting systems increases." Which law of thermodynamics does this statement refer to?

Second law of thermodynamics

First law of thermodynamics

Third law of thermodynamics

Zeroth law of thermodynamics

Explanation

There are four main laws of thermodynamics, which describe how temperature, energy, and entropy behave under various circumstances. The zeroth law of thermodynamics helps to define temperature; it states that if two systems are each in thermal equilibrium with a third system, they must be in thermal equilibrium with each other. The first law of thermodynamics negates the possibility of perpetual motion; it states that when energy passes into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. The second law of thermodynamics also negates the possibility of perpetual motion; it states that in a natural thermodynamic process, the sum of the entropies of the interacting systems increases. Lastly, the third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature nears absolute zero.

Calculating heat

How much heat is absorbed by a copper penny as it warms from $-12^{\circ}C$ to $43^{\circ}C$ assuming the penny is pure copper with a mass of ? $C_{s}$ of copper is $.385\frac{J}{g^\circ C}$ .

Explanation

Use the equation that relates heat, mass, specific heat, and change in temperature:

$q=mC\Delta T$

$\Delta T=T_{f}-T_{i}=43C-(-12C)=55C$

$q=2.5g*.385\frac{J}{g*C}*55C=52.94J$

Which of the following statements is true of standard states?

Gas at pressure

Solute of concentration

Temperature at $100 ^{\circ} C$

Gas at

Solute in of solution

Explanation

Standard states are defined as a specific set of conditions, such as when a gas is at , concentration, and $25^{\circ} C$ .

Standard enthalpy of formation, the energy required for form 1 mole of a compound from its constituent elements, occurs when elements are in their standard states.

The second law of thermodynamics states which of the following is true regarding an isolated system?

The entropy can only increase

The entropy can only decrease

Energy in the form of heat is always conserved

Two systems in thermal equilibrium with a third system are in thermal equilibrium with each other

The entropy approaches a constant value as the temperature of the system approaches zero Kelvin

Explanation

The entropy cannot decrease in an isolated system because the energy can only be degraded. Since the system is isolated, no higher-grade energy—or any energy at all—is being introduced into the system. As a result, the entropy cannot decrease. The other answer choices relate to the other laws of thermodynamics.

How much heat is required to raise the temperature of of water from $13^{\circ} C$ to $100^{\circ} C$ ? (Specific heat capacity of water is $4.18 J g^{-1}^{\circ}C^{-1}$ )