Consider the following reaction at equilibrium:

$$2 \mathrm{H}_2(g)+\mathrm{S}_2(g) \rightleftarrows 2 \mathrm{H}_2 \mathrm{~S}(g)+\text { heat }$$

In a 10.0-L container, an equilibrium mixture contains $2.02 \mathrm{~g}$ of $\mathrm{H}_2, 10.3 \mathrm{~g}$ of $\mathrm{S}_2$, and $68.2 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{~S}$. (7.1, 7.2, 13.2, 13.3, $13.4,13.5)$ a. What is the numerical value of $K_{\mathrm{c}}$ for this equilibrium mixture? b. If more $\mathrm{H}_2$ is added to the equilibrium mixture, how will the equilibrium shift? c. How will the equilibrium shift if the mixture is placed in a 5.00-L container with no change in temperature? d. If a 5.00-L container has an equilibrium mixture of $0.300 \mathrm{~mol}$ of $\mathrm{H}_2$ and $2.50 \mathrm{~mol}$ of $\mathrm{H}_2 \mathrm{~S}$, what is the $\left[\mathrm{S}_2\right]$ if temperature remains constant?

Calculate the work required to stretch the following springs 1.25 m from their equilibrium positions. Assume Hooke's law is obeyed. A spring that requires a force of $250 \mathrm{~N}$ to be stretched $0.5 \mathrm{~m}$ from its equilibrium position.

The supply function for a product is given by $p=0.1 q^2+50 q+1027.50$ and the demand function for this product is p=6000-20q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity.

Show that the system

$$\begin{array}{l}{x^{\prime}=y} \\ {y^{\prime}=-\sin x-y}\end{array}$$

has an equilibrium point at the origin. Compute the Jacobian, then discuss the type and stability of the equilibrium point. Find and describe other equilibria if they exist.

The following diagrams represent the equilibrium state for three different reactions of the type $\mathrm{A}+\mathrm{X} \rightleftharpoons \mathrm{AX}(\mathrm{X}=\mathrm{B}, \mathrm{C}$, or $\mathrm{D})$ :
Which reaction has the largest equilibrium constant?

A pendulum swings back and forth. How many times does it pass through the equilibrium position during one cycle of its motion? Assume the cycle begins when the pendulum is at maximum displacement from equilibrium.

Assume that the gold-mining industry is competitive.

Illustrate a long-run equilibrium using diagrams for the gold market and for a representative gold mine.

Consider the gas-phase reaction 2 CO (g) + O2 (g) <=> 2 CO2 (g) Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture (a) at constant pressure and (b) at constant volume.

Consider the combustion of methane (as represented by the following equation). This is the reaction that occurs for a Bunsen burner, which is a source of heat for chemical reactions in the laboratory.

$$\mathrm{CH}_4(g)+2 \mathrm{O}_2(g) \rightleftharpoons \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(g)$$

For the system at chemical equilibrium, which of the following explains what happens if the temperature is raised? a. The equilibrium position is shifted to the right, and the value for $K$ decreases.
b. The equilibrium position is shifted to the left, and the value for $K$ decreases.
c. The equilibrium position is shifted to the left, and the value for $K$ increases.
d. The equilibrium position is shifted, but the value for $K$ stays constant.

Assume that the gold-mining industry is competitive.

a. Illustrate a long-run equilibrium using diagrams for the gold market and for a representative gold mine.

b. Suppose that an increase in jewelry demand induces a surge in the demand for gold. Using your diagrams, show what happens in the short run to the gold market and to each existing gold mine.

c. If the demand for gold remains high, what would happen to the price over time? Specifically, would the new long-run equilibrium price be above, below, or equal to the short-run equilibrium price in part (b)? Is it possible for the new long-run equilibrium price to be above the original long-run equilibrium price? Explain.

What is true about gradualism with respect to punctuated equilibrium?

a. Each is a model of evolution.

b. Neither is a model of evolution.

c. Only gradualism portrays true evolution.

d. Only punctuated equilibrium portrays true evolution.

An insulated Thermos contains 150 g of water at

$$80.0 ^ { \circ } \mathrm { C }$$

. You put in a 12.0 g ice cube at

$$0 ^ { \circ } \mathrm { C }$$

to form a system of ice + original water. (a) What is the equilibrium temperature of the system? What are the entropy changes of the water that was originally the ice cube (b) as it melts and (c) as it warms to the equilibrium temperature? (d) What is the entropy change of the original water as it cools to the equilibrium temperature? (e) What is the net entropy change of the ice + original water system as it reaches the equilibrium temperature?

The hydrogen sulfite ion, $\mathrm{HSO}_{3}^{-}$, is a weak acid in aqueous solution. Write an equation showing the equilibrium established when hydrogen sulfite is dissolved in aqueous solution, using unequal arrows to show the equilibrium.

The following picture represents an equilibrium mixture of solid $\mathrm{BaCO}_3$ solid $\mathrm{BaO}$, and gaseous $\mathrm{CO}_2$ obtained as a result of the endothermic decomposition of $\mathrm{BaCO}_3$ : (a) Draw a picture that represents the equilibrium mixture after addition of four more $\mathrm{CO}_2$ molecules. (b) Draw a picture that represents the equilibrium mixture at a higher temperature.