Thermodynamics | Practice Problems, Examples & Solutions

Spontaneity

Physical Chemistry

For the reaction $\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g})=2 \mathrm{NH}_{3}(\mathrm{g}), K=1.60 \times$
$10^{-4}$ at $400^{\circ} \mathrm{C} .$ Calculate $(a) \Delta_{\tau} G^{\circ}$ and $(b) \Delta_{\mathrm{r}} G$ when the pressures of $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$ are maintained at 10 and 30 bar, respectively, and $\mathrm{NH}_{3}$ is removed at a partial pressure of 3 bar. $(c)$ Is the reaction spontaneous under the latter conditions?

Chemical Equilibrium

03:12

Biochemistry

Consider the equation $\Delta G=\Delta H-T(\Delta S)$.
Why is the entropy of a system dependent on temperature?

Biochemistry and the Organization of Cells

01:31

Introduction to General, Organic and Biochemistry

Consider the following equilibrium reaction. Under each species is its equilibrium concentration. Calculate the equilibrium constant for the reaction.
$$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$

Reaction Rates and Chemical Equilibrium

Entropy

134 Practice Problems

01:04

Physical Chemistry

An ideal monatomic gas is heated from 300 to $1000 \mathrm{K}$ and the pressure is allowed to rise from 1 to 2 bar. What is the change in molar entropy?

Second and Third Laws of Thermodynamics

03:33

Physical Chemistry

A mixture of $\mathrm{H}_{2}$ and $\mathrm{NH}_{3}$ has a volume of $139.0 \mathrm{cm}^{3}$ at $0.00^{\circ} \mathrm{C}$ and 1 atm. The mixture is cooled to the temperature of liquid nitrogen at which ammonia freezes out and the remaining gas is removed from the vessel. Upon warming the vessel to $0.00^{\circ} \mathrm{C}$ and 1 atm, the volume is $77.4 \mathrm{cm}^{3}$. Calculate the mole fraction of $\mathrm{NH}_{3}$ in the original mixture.

Fundamental Concepts of Thermodynamics

01:37

Introduction to General, Organic and Biochemistry

In photosynthesis, light energy from the sun is used to produce sugars. How does this process represent a conversion of energy from one form to another?

Matter, Energy, and Measurement

2nd Law of Thermodynamics

76 Practice Problems

01:16

Introduction to General, Organic and Biochemistry

If a reaction is very exothermic-that is, if the products have a much lower energy than the reactants-can we be reasonably certain that it will take place rapidly?

Reaction Rates and Chemical Equilibrium

0:00

Biochemistry

Show that the transfer of heat from an object of higher temperature to one of lower temperature, but not the reverse process, obeys the second law of thermodynamics.

Thermodynamic Principles: A Review

02:04

General Chemistry: Principles and Modern Applications

The reaction, $$2 \mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$ $$\Delta_{r} H^{\circ}=$$ $-161 \mathrm{kJmol}^{-1},$ is expected to be (a) spontaneous at all temperatures; (b) spontaneous at low temperatures, but nonspontaneous at high temperatures;
(c) nonspontaneous at all temperatures; (d) spontaneous at high temperatures only.

Spontaneous Change: Entropy and Gibbs Energy

3rd Law of Thermodynami

5 Practice Problems

04:30

Chemistry

Under what conditions does a substance have a standard entropy of zero? Can a substance ever have a negative standard entropy?

Entropy, Free Energy, and Equilibrium

01:40

Chemistry

State the third law of thermodynamics and explain its usefulness in calculating entropy values.

Entropy, Free Energy, and Equilibrium

02:41

Chemistry and Chemical Reactivity

The third law of thermodynamics says that a perfect crystal at 0 K has zero entropy. The standard entropy of a substance, $S^{\circ}$ can be determined by evaluating the energy required to carry out conversion from 0 K to standard conditions. What information would be needed to calculate $S^{\circ}$ for liquid water at $298 \mathrm{K}$ and 1 bar?

Principles of Chemical Reactivity: Entropy and Free Energy

Gibbs Free Energy

80 Practice Problems

03:00

Physical Chemistry

The surface tension of water is $71.97 \times 10^{-3} \mathrm{Nm}^{-1}$ or $71.97 \times 10^{-3} \mathrm{Jm}^{-2}$ at $25^{\circ} \mathrm{C}$. Calculate the surface energy in joules of 1 mol of water dispersed as a mist containing droplets of $1 \mu \mathrm{m}\left(10^{-4} \mathrm{cm}\right)$ in radius. The density of water may be taken as $1.00 \mathrm{g} \mathrm{cm}^{-3}$.

First Law of Thermodynamics

06:31

Physical Chemistry

Under anaerobic conditions, glucose is broken down in muscle tissue to form lactic acid according to the reaction: $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{CH}_{3} \mathrm{CHOHCOOH}(a q) .$ Thermodynamic data at $T=298 \mathrm{K}$ for glucose and lactic acid are given in the following table.
Calculate $\Delta G_{R}^{\circ}$ at $T=298 \mathrm{K} .$ and $T=310 .$ K. In your calculation at $310 . \mathrm{K},$ assume (a) that $\Delta H_{R}^{\circ}$ and $\Delta S_{R}^{\circ}$ are constant in this temperature interval and (b) calculate $\Delta H_{R}^{\circ}$ and $\Delta S_{R}^{\circ}$ at
310. K using the data in the previous table. Assume all heat capacities are constant in this temperature interval.

Chemical Equilibrium

03:32

Physical Chemistry

You have containers of pure $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ at $298 \mathrm{K}$ and 1 atm pressure. Calculate $\Delta G_{\text {mixing}}$ relative to the unmixed gases of a. a mixture of $10 .$ mol of $\mathrm{O}_{2}$ and $10 .$ mol of $\mathrm{N}_{2}$
b. a mixture of $10 .$ mol of $\mathrm{O}_{2}$ and $20 .$ mol of $\mathrm{N}_{2}$
c. Calculate $\Delta G_{\text {mixing}}$ if $10 .$ mol of pure $\mathrm{N}_{2}$ is added to the mixture of $10 .$ mol of $\mathrm{O}_{2}$ and $10 .$ mol of $\mathrm{N}_{2}$

Chemical Equilibrium