Problem 82 - Chemistry The Science in Context

Question

Ammonium hydrogen sulfide (NH_4SH) has been detected in the atmosphere of Jupiter. The equilibrium between ammonia, hydrogen sulfide, and \(\mathrm{NH}_{4} \mathrm{SH}\) is described by the following equation: $$ \mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) $$ The value of \(K_{\mathrm{p}}\) for the reaction at \(24^{\circ} \mathrm{C}\) is \(0.126 .\) Suppose a sealed flask contains an equilibrium mixture of \(\mathrm{NH}_{4} \mathrm{SH}\), \(\mathrm{NH}_{3},\) and \(\mathrm{H}_{2} \mathrm{S}\) at \(24^{\circ} \mathrm{C} .\) At equilibrium, the partial pressure of \(\mathrm{H}_{2} \mathrm{S}\) is 0.355 atm. What is the partial pressure of \(\mathrm{NH}_{3} ?\)

Step-by-Step Solution

Answer

Answer: The partial pressure of NH_3 at equilibrium is 0.355 atm.

Step 1: Write the equilibrium expression

The equilibrium expression for the given reaction can be written as: $$ K_p = \frac{[NH_3(g)][H_2S(g)]}{[NH_4SH(s)]} $$ However, the concentration of solid substances, in this case [NH_4SH], does not affect the equilibrium constant. So we can rewrite the expression as: $$ K_p = [NH_3(g)][H_2S(g)] $$

Step 2: Define the variables

Let's define the variables for the equilibrium pressures: Let $$P_{NH_3}$$ be the partial pressure of NH_3, and we know $$P_{H2S} = 0.355 atm $$. Now we can write the expression for K_p in terms of these partial pressures: $$ K_p = P_{NH_3} \times P_{H2S} $$

Step 3: Substitute the known values and solve for the unknown

We know the value of K_p and the partial pressure of H_2S. We can substitute these values in the equation and solve for the partial pressure of NH_3: $$ 0.126 = P_{NH_3} \times 0.355 $$ Now, divide both sides by 0.355 to isolate the partial pressure of NH_3: $$ P_{NH_3} = \frac{0.126}{0.355} $$

Step 4: Calculate the partial pressure of NH_3

Now, plug in the values and solve for the partial pressure of NH_3: $$ P_{NH_3} = \frac{0.126}{0.355} = 0.355 $$ The partial pressure of NH_3 at equilibrium is 0.355 atm.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as K or K_eq, is a value that represents the ratio of the concentration of products to reactants at the point when a chemical reaction has reached equilibrium. This constant is crucial as it gives an indication of the position of equilibrium. The higher the value of K, the more the reaction favors the formation of products.

For gas-phase reactions, we often use the equilibrium constant in terms of partial pressures, denoted as K_p. It involves the partial pressures of the gaseous products and reactants. The equilibrium constant expression is derived from the balanced chemical equation and follows the law of mass action.

To calculate K_p, it's important to remember that the concentration of solids, like ammonium hydrogen sulfide (NH_4SH) in our exercise, does not change during the reaction and therefore does not appear in the K_p expression. Only gaseous substances are included, making the equilibrium constant a critical indicator of the extent of the reaction for volatile substances like NH_3 and H_2S found in our Jupiter atmosphere example.

Partial Pressure

Partial pressure is a term used in chemistry to describe the pressure contributed by an individual gas in a mixture of gases. Each gas in a mixture exerts pressure independently as if the other gases were not present. The total pressure of the mixture is the sum of the individual partial pressures.

This concept is fundamental in understanding gas-phase reactions. For instance, in our exercise, the reaction involves ammonia (NH_3) and hydrogen sulfide (H_2S) gases. The partial pressure of each gas is a part of the equilibrium constant expression for the reaction. At equilibrium, we are given the partial pressure of H_2S, but we need to find the partial pressure of NH_3. By applying Dalton's Law of Partial Pressures and the equilibrium constant, we were able to compute this unknown quantity, allowing us to better understand the distribution of particles in our sealed flask.

Gas-phase Reactions

Chemical reactions involving substances in the gas phase are referred to as gas-phase reactions. These reactions are marked by the interactions between gaseous reactants to form product gases. The behavior and rate of these reactions can be influenced by factors such as temperature, pressure, and volume.

In the exercise, the reaction involves ammonium hydrogen sulfide breaking down into ammonia and hydrogen sulfide gases, fitting succinctly into the category of gas-phase reactions. Understanding these reactions is vital for discerning atmospheric compositions, such as that of Jupiter, where gas-phase chemistry plays a dominant role. The equilibrium between gaseous substances is essential for predicting the outcome and understanding the nature of the atmosphere or any closed system involving gaseous reactants and products.