(a) A reaction has a standard free-energy change of -14.6 kJ$\mathrm{~mol}^{-1}$. Calculate the equilibrium constant for the reaction at $25^{\circ} \mathrm{C}$. (b) Calculate the standard free-energy difference between starting materials and products for a reaction that has an equilibrium constant of 305.

Write a paragraph explaining how fungi either maintain or disrupt the equilibrium of an ecosystem. Use examples.

Suppose a reaction has the equilibrium constant $K=4.5\times 10^{-6}$ at a particular temperature. If an experiment is set up with this reaction, will there be large relative concentrations of products present at equilibrium? Is this reaction useful as a means of producing the products? How might the reaction be made more useful?

Consider the gas-phase reaction

$$2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}_2(\mathrm{~g})$$

Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture
at constant volume.

Rent controls on apartments are an example of price controls on a commodity. They keep the price artificially low (below the equilibrium price). Sketch a graph of supply and demand curves, and label on it a price $p^{-}$ below the equilibrium price. What effect does forcing the price down to $p^{-}$ have on: The producer surplus?

A $1.3\text{~kg}$ mass is attached to a spring with a force constant of $52 \mathrm{~N} / \mathrm{m}$. If the mass is released with a speed of $0.28 \mathrm{~m} / \mathrm{s}$ at a distance of $8.1 \mathrm{~cm}$ from the equilibrium position of the spring, what is its speed when it is halfway to the equilibrium position?

At $25^{\circ} \mathrm{C}$, the equilibrium partial pressures of $\mathrm{NO}_2$ and $\mathrm{N}_2 \mathrm{O}_4$ are $0.15 \mathrm{~atm}$ and $0.20 \mathrm{~atm}$, respectively. If the volume is doubled at constant temperature. Calculate the partial pressures of the gases when a new equilibrium is established.

Consider the equilibrium

$$\mathrm { Na } _ { 2 } \mathrm { O } ( s ) + \mathrm { SO } _ { 2 } ( g ) \rightleftharpoons \mathrm { Na } _ { 2 } \mathrm { SO } _ { 3 } ( s )$$

All the compounds in this reaction are soluble in water. Rewrite the equilibrium-constant expression in terms of molarities for the aqueous reaction.

Work the following exercise.

Let the supply and demand for sugar be given by

supply: p = 1.4 q-.6 and demand: p = -2 q+3.2

where p is in dollars.

(a) Graph these on the same axes.

(b) Find the equilibrium quantity.

(c) Find the equilibrium price.

(d) On what interval does supply exceed demand?

A weight attached to a spring is pulled down 2 inches below the equilibrium position. What is the frequency?

Rent controls on apartments are an example of price controls on a commodity. They keep the price artificially low (below the equilibrium price). Sketch a graph of supply and demand curves, and label on it a price $p^{-}$ below the equilibrium price. What effect does forcing the price down to $p^{-}$ have on: The consumer surplus?

Solid aluminum phosphate, $\mathrm{AlPO}_{4}$, is in equilibrium with its ions in solution: $\mathrm{AlPO}_{4} \rightleftarrows \mathrm{Al}^{3+}+\mathrm{PO}_{4}^{3-}$ with $K_{\mathrm{sp}}=10^{-22}$ Find the equilibrium concentration of phosphate ions (in mg/L).

Draw a correctly labeled graph for a land market in which land is in fixed supply. Label each of the following on your graph: the axes, the supply and demand curves for land, the equilibrium rental rate, and the equilibrium quantity of land employed. Shade and label the area that represents economic rent.

How will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?