Describe why it is easier to use $\Delta G$ to determine the spontaneity of a process rather than $\Delta S_{\mathrm{u}}$.

Consider the reaction

$$\mathrm{CS}_2(g)+4 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(g)+2 \mathrm{H}_2 \mathrm{~S}(\mathrm{~g})$$

Calculate $\Delta H^{\circ}, \Delta S^{\circ}$, and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for this reaction. Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are constant with respect to a change of temperature. Now calculate $\Delta G^{\circ}$ at $650^{\circ} \mathrm{C}$. Compare the two values of $\Delta G^{\circ}$. Briefly discuss the spontaneity of the reaction at $25^{\circ} \mathrm{C}$ and at $650^{\circ} \mathrm{C}$.

Letting h(x)=f(x)+g(x), say which of the following statements must be true. Briefly explain your reasoning.

(a) If $f$ and $g$ have the same domain, so does $h$.

(b) If $f$ and $g$ have the same range, so does $h$.

(c) If $f$ and $g$ lack zeros, so does $h$.

(d) Where defined, $\frac{\Delta h}{\Delta x}=\frac{\Delta f}{\Delta x}+\frac{\Delta g}{\Delta x}$.

What conveniences do catalogs offer?

Each of the following sets is the solution of an inequality of the form $|x − c |< \delta$. Find $c$ and $\delta$.

$(-3,7)$.

Choose the correct answer.

Area lying in the first quadrant and bounded by the circle x^2 + y^2 = 4 and the lines x = 0 and x = 2 is

(A) pi

(B) pi/2

(C) pi/3

(D) pi/4

Find the slope and $y$-intercept of each equation. $y=-2 x+1$

Use a calculator to evaluate the function. Round to four decimal places.

$$\tan 192^{\circ}$$

Identify the slope, $m$, and the $y$-intercept, $b$, for each line. Then graph.

$$x+y=6$$

Find the exact value of each expression given below.

a. $\cos \frac{5 \pi}{6}$

b. $\sin \frac{5 \pi}{6}$

c. $\tan \frac{5 \pi}{6}$

d. $\csc \frac{5 \pi}{6}$

e. $\cos \frac{11 \pi}{6}$

f. $\cos \left(-\frac{\pi}{6}\right)$

What is the name of Cl$_2$O$_3$?

Till, moraine and kettle are examples of:

A. glacial erosion

B. glacial deposition

C. types of glaciers

D. valley glaciers

Please select the best answer from the choices provided.

Simplify each of the following.

$$\cos \left(\frac{\pi}{4}-x\right) \sec \frac{\pi}{4}-\sin \left(\frac{\pi}{4}-x\right) \csc \frac{\pi}{4}$$

Determine the following:

a) $\bigcup_{n=1}^{\infty}\left\{\sin ^2 \frac{n \pi}{2}+\cos ^2 \frac{n \pi}{2}\right\}$ and $\bigcap_{n=1}^{\infty}\left\{\sin ^2 \frac{n \pi}{2}+\cos ^2 \frac{n \pi}{2}\right\}$

b) $\bigcup_{n=1}^{\infty}\left\{\sin \frac{n \pi}{2}+\cos \frac{n \pi}{2}\right\}$ and $\bigcap_{n=1}^{\infty}\left\{\sin \frac{n \pi}{2}+\cos \frac{n \pi}{2}\right\}$