The degree of dissociation, $\alpha,$ of $\mathrm{CO}_{3}(\mathrm{g})$ into CO(g) and $\mathrm{O}_{2}(\mathrm{g})$ at high temperatures and 1 bar total pressure was found to vary with temperature as follows:

$$\begin{matrix} \text{$T / K$} & \text{1395} & \text{1443} & \text{1498}\\ \text{$\alpha / 10^{-4}$} & \text{1.44} & \text{2.5} & \text{4.71}\\ \end{matrix}$$

Assume $\Delta_{r} H^{0}$ to be constant over this temperature range, and calculate K, $\Delta_{r} G^{0}, \Delta_{r} H^{0},$ and $\Delta_{r} S^{0}$ at 1443 K. Make any justifiable approximations.

You have two temperature gages available to you. One measuring 100-500$^{\circ}$C and the other with a range of 100-1000$^{\circ}$C. Each has an uncertainty of 2 % of its span. To measure a temperature of about 300$^{\circ}$C, which of the two will you choose? Why?

Imagine you have a close family member who bicycles to work on major streets during rush hour. During this time, air pollution is at its worst, and a cyclist inhales a lot of it. Write a dialogue in which you encourage the family member to consider the negative effects of this practice. Explain the problems that can result.

Evaluate each expression for the given values of the variable.

$$\frac { y ( y - 3 ) } { y - 2 }$$

y=4

Estimate $\Delta H$ and $\Delta S$ if the temperature of $1.75$ moles of $\mathrm{Hg}(l)$ is increased from $0.00^{\circ} \mathrm{C}$ to $75.0^{\circ} \mathrm{C}$ at $1\ \text{bar}$. Over this temperature range, $C_{P, m}\left(\mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)=$ $30.093-4.944 \times 10^{-3} T / \mathrm{K}$.

The following equation can be used to relate the density of liquid water to Celsius temperature in the range from $0^{\circ} \mathrm{C}$ to about $20^{\circ} \mathrm{C}$ :

d$\left(\mathrm{g} / \mathrm{cm}^3\right)=\frac{0.99984+\left(1.6945 \times 10^{-2} t\right)-\left(7.987 \times 10^{-6} t^2\right)}{1+\left(1.6880 \times 10^{-2} t\right)}$

At what temperature does water have a density of $0.99860 \mathrm{~g} / \mathrm{cm}^3$ ?

There is a relationship between the number of times a cricket chirps and the air temperature. The function $f(C)=7 C-30$, where $C$ is the temperature in degrees Celsius, can be used to approximate the number of times per minute that a cricket chirps. Discuss the domain and range of this function, and explain the significance of its $x$-intercept.

Calculate $\Delta H$ and $\Delta S$ if the temperature of $1.75\ moles$ of $\mathrm{Hg}(l)$ is increased from $0.00^{\circ} \mathrm{C}$ to $75.0^{\circ} \mathrm{C}$ at $1\ bar$. Over this temperature range, $C_{P, m}\left(\mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)=$ $30.093-4.944 \times 10^{-3} \mathrm{~T} / \mathrm{K}$.

When two ideal gases are mixed, they must have the same average molecular speed when they have reached thermal equilibrium.

A mass of $32.0 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}(g)$ at $373 \mathrm{~K}$ is flowed into $295 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}(l)$ at $310 . \mathrm{K}$ and $1 \mathrm{~atm}$. Estimate the final temperature of the system once equilibrium has been reached. Assume that $C_{P, m}$ for $\mathrm{H}_{2} \mathrm{O}(l)$ is constant at its values for $298 \mathrm{~K}$ throughout the temperature range of interest. Describe the state of the system.

Evaluate the line integral

$$\int\limits_C xe^yds,$$

where $C$ is the line segment from $(2,0)$ to $(5,4)$.

In the following sentence, choose the letter of the correct word.

He went on working oblivious (a) from, (b) to the surrounding chaos.

Choose the correct answer.

Dame Judi Dench is considered to be one of the (a) classyest, (b) classiest actors working today.

identify and sketch the graph of the conic section. $\frac{x^{2}}{9}-\frac{y^{2}}{16}-1=0$