Iodine is sparingly soluble in water but much more so in carbon tetrachloride $\left(\mathrm{CCl}_4\right)$. The equilibrium constant, also called the partition coefficient, for the distribution of $\mathrm{I}_2$ between these two phases

$$\mathrm{I}_2(a q) \rightleftharpoons \mathrm{I}_2\left(\mathrm{CCl}_4\right)$$

is 83 at $20^{\circ} \mathrm{C}$. (b) The student now repeats the extraction of $\mathrm{I}_2$ with another $0.030 \mathrm{~L}$ of $\mathrm{CCl}_4$. Calculate the fraction of the $\mathrm{I}_2$ from the original solution that remains in the aqueous phase.

Use the van't Hoff equation in above Problem to derive the following expression, which relates the equilibrium constants at two different temperatures

$$\ln \frac{K_1}{K_2}=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$$

How does this equation support the prediction based on Le Chatelier's principle about the shift in equilibrium with temperature?

Consider the equilibrium between molecular oxygen and ozone

$$3 \mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{O}_3(g) \quad \Delta H^{\circ}=284 \mathrm{~kJ} / \mathrm{mol}$$

What would be the effect of (a) increasing the pressure on the system by decreasing the volume, (b) adding $\mathrm{O}_2$ to the system, (c) decreasing the temperature, and (d) adding a catalyst?

Write the equation relating $K_{\mathrm{c}}$ and $K_P$ and define all the terms.

Define equilibrium. Give 2 examples of a dynamic equilibrium.

From the following equilibrium constant expression, write a balanced chemical equation for the gas-phase reaction. Does $K_{\mathrm{c}}=K_P$ for this reaction?

$$K_{\mathrm{c}}=\frac{\left[\mathrm{NH}_3\right]^2\left[\mathrm{H}_2 \mathrm{O}\right]^4}{\left[\mathrm{NO}_2\right]^2\left[\mathrm{H}_2\right]^7}$$

Write $K_{\mathrm{c}}$ and $K_P$ for the decomposition of dinitrogen pentoxide:

$$2 \mathrm{N}_2 \mathrm{O}_5(g) \rightleftharpoons 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$

Consider the equilibrium $\mathrm{X} \rightleftharpoons \mathrm{Y}$, where the forward reaction rate constant is greater than the reverse reaction rate constant. Which of the following is true about the equilibrium constant? (a) $K_{\mathrm{c}}>1$, (b) $K_{\mathrm{c}}<1$, (c) $K_{\mathrm{c}}=1$.

Use synthetic division to determine if the given value for k is a zero of the corresponding polynomial. If not, determine $p(k)$.

$$p(x)=18 x^5-87 x^4+110 x^3-28 x^2-16 x+3 ; k=\dfrac{2}{3}$$

For the following exercises, write the first five terms of the geometric sequence. $a_{n}=-4 \cdot 5^{n-1}$

Write the phrase as an algebraic expression. Use the variable $x$ to represent the unknown number.

The difference of twenty-five and a number.

Write the sum of the series as the ratio of two integers.

$$0 . \overline{01}$$

Su mamá comenta cómo Ud. y sus hermanos hacen los quehaceres de la casa. Escriba lo que ella dice, usando los comparativos por turnos.

EJEMPLO: lavar los platos  Gloria lava los platos mejor (peor) que yo.

cocinar ___________________

Is the statement true or false? Assume that y = f(x) is a solution to the equation dy/dx = g(x). If the statement is true, explain how you know. If the statement is false, give a counterexample. If $\lim _{x \rightarrow \infty} g(x)=\infty,$ then $\lim _{x \rightarrow \infty} f(x)=\infty.$