Problem 35 - Chemistry: An Atoms-Focused Approach

Question

For which of the following reactions are the values of \(K_{c}\) and \(K_{\mathrm{p}}\) equal? a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) b. \(F e(s)+C O_{2}(g) \rightleftarrows F e O(s)+C O(g)\) c. \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\)

Step-by-Step Solution

Answer

a) 2SO2(g) + O2(g) ⇌ 2SO3(g) b) Fe(s) + CO2(g) ⇌ FeO(s) + CO(g) c) H2O(g) + CO(g) ⇌ H2(g) + CO2(g) Answer: Reactions b and c have equal Kc and Kp values.

Step 1: Reaction a

For reaction a, the balanced chemical equation is \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\). Counting moles of gas in reactants and products, we have: Reactants: 2 moles of SO2 + 1 mole of O2 = 3 moles of gas Products: 2 moles of SO3 = 2 moles of gas In this case, the number of moles of gas is not equal in reactants and products, so Kc is not equal to Kp for this reaction.

Step 2: Reaction b

For reaction b, the balanced chemical equation is \(F e(s)+C O_{2}(g) \rightleftarrows F e O(s)+C O(g)\). Counting moles of gas in reactants and products, we have: Reactants: 1 mole of CO2 = 1 mole of gas Products: 1 mole of CO = 1 mole of gas In this case, the number of moles of gas is equal in reactants and products, so Kc is equal to Kp for this reaction.

Step 3: Reaction c

For reaction c, the balanced chemical equation is \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\). Counting moles of gas in reactants and products, we have: Reactants: 1 mole of H2O + 1 mole of CO = 2 moles of gas Products: 1 mole of H2 + 1 mole of CO2 = 2 moles of gas In this case, the number of moles of gas is equal in reactants and products, so Kc is equal to Kp for this reaction. In conclusion, the values of Kc and Kp are equal for reactions b and c.

Key Concepts

Chemical Equilibrium

Chemical equilibrium in a reaction is reached when the rate of the forward reaction equals the rate of the reverse reaction. This results in concentrations of reactants and products remaining constant over time, though not necessarily equal. It is important to understand that even when equilibrium is achieved, reactions have not stopped completely.
They continue to occur, but at the same rate.In chemical equilibrium, we often refer to two constants:

• Equilibrium constant for concentration, denoted as \(K_c\).
• Equilibrium constant for pressure, denoted as \(K_p\) when dealing with gases.

The relationship between \(K_c\) and \(K_p\) depends on the change in the number of moles of gas during the reaction. If there is no change in moles of gas, then \(K_c = K_p\). When writing equilibrium expressions, the concentrations are used for \(K_c\) and partial pressures for \(K_p\).

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It refers to using balanced chemical equations to determine the relationships between the different molecules involved.When chemical equations are balanced, it shows the smallest whole number ratio of moles of reactants to products. This is crucial for predicting the amounts of products formed from given quantities of reactants or vice versa.
For example, in the reaction \(2 \text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2 \text{SO}_3(g)\), the stoichiometry tells us that two moles of \(\text{SO}_2\) react with one mole of \(\text{O}_2\) to produce two moles of \(\text{SO}_3\). The coefficients also give insights into the volume ratios when dealing with gases at constant temperature and pressure.

Gas Moles Balance

Gas moles balance is an important concept when considering reactions involving gases. It involves counting and comparing the moles of gas on both sides of a balanced chemical equation.Why this matters comes down to the relationship between \(K_c\) and \(K_p\). For gases, changing the number of moles alters the volume and pressure, so it directly influences \(K_p\).

• If the number of moles of gas is the same on both sides of the reaction, \(\Delta n = 0\), where \(\Delta n\) is the change in moles.
• This means \(K_c\) equals \(K_p\) because the ratio \((RT)^{\Delta n}\) is \(1\).

In reactions b and c from the exercise, we observed this equality of gas moles:- Reaction b: 1 mole of gas on reactants and products sides- Reaction c: 2 moles of gas on reactants and products sidesThus ensuring \(K_c\) is equal to \(K_p\). Understanding gas moles balance simplifies many calculations in reactions involving gases and equilibrium constants.