The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_2(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous and has a negative value for $\Delta S^{\circ}$. The second law of thermodynamics states that in any spontaneous process there is always an increase in the entropy of the universe. Is there an inconsistency between the above reaction and the second law?

For each of the following processes, indicate whether the signs of

$$\Delta S$$

and

$$\Delta H$$

are expected to be positive, negative, or about zero. Ethyl alcohol evaporates from a beaker.

For each of the following processes, indicate whether the signs of

$$\Delta S$$

and

$$\Delta H$$

are expected to be positive, negative, or about zero. The temperature of a sample of Co(s) is lowered from

$$60 ^ { \circ } \mathrm { C }$$

to

$$25 ^ { \circ } \mathrm { C }$$

For each of the following processes, indicate whether the signs of

$$\Delta S$$

and

$$\Delta H$$

are expected to be positive, negative, or about zero. A solid sublimes.

Indicate whether each of the following statements is true or false. If it is false, correct it. Spontaneous processes in general require that work be done to force them to proceed.

Indicate whether each of the following statements is true or false. If it is false, correct it. The reaction of Na(s) with

$$Cl_2(g)$$

to form NaCl(s) is a spontaneous process.

Indicate whether each of the following statements is true or false. If it is false, correct it. The feasibility of manufacturing

$$NH_3$$

from

$$N_2$$

and

$$H_2$$

depends entirely on the value of

$$\Delta H$$

for the process

$$\mathrm { N } _ { 2 } ( g ) + 3 \mathrm { H } _ { 2 } ( g ) \longrightarrow 2 \mathrm { NH } _ { 3 } ( g )$$

The $K_6$ for methylamine $\left(\mathrm{CH}_3 \mathrm{NH}_2\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix $\mathrm{D}$.

What is the value of $\Delta G$ at equilibrium?

The $K_6$ for methylamine $\left(\mathrm{CH}_3 \mathrm{NH}_2\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix $\mathrm{D}$.

By using the value of $K_b$, calculate $\Delta G^{\circ}$ for the equilibrium in part (a).

For a reversible isothermal process, write an expression for

$$\Delta E$$

in terms of q and w and an expression for

$$\Delta S$$

in terms of q and T.

The $K_6$ for methylamine $\left(\mathrm{CH}_3 \mathrm{NH}_2\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix $\mathrm{D}$.

Write the chemical equation for the equilibrium that corresponds to $K_b$.

Which depend on the path taken from one state to another?

For a reversible isothermal process, write an expression for $\Delta E$ in terms of q and wand an expression for $\Delta S$ in terms of q and T.

The value of $\mathrm{K}_{\mathrm{a}}$ for nitrous acid $\left(\mathrm{HNO}_2\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix $D$.

What is the value of $\Delta G$ when $\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-2} \mathrm{M},\left[\mathrm{NO}_2{ }^{-}\right]=6.0 \times 10^{-4} \mathrm{M}$, and $\left[\mathrm{HNO}_2\right]=0.20 \mathrm{M}$ ?