Chapter 13: Problem 47

At a particular temperature, $12.0$ moles of $\mathrm{SO}_{3}$ is placed into a 3.0-L rigid container, and the $\mathrm{SO}_{3}$ dissociates by the reaction $$ 2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) $$ At equilibrium, $3.0$ moles of $\mathrm{SO}_{2}$ is present. Calculate $K$ for this reaction.

Short Answer

Expert verified

The equilibrium constant (K) for the reaction is 0.056.

Step by step solution

Initially, we have 12.0 moles of SO3, and at equilibrium, we have 3.0 moles of SO2. From the balanced reaction, we know that for every 2 moles of SO3 that dissociate, 2 moles of SO2 and 1 mole of O2 forms. Let's determine the change in moles for each gas in the reaction. Change in moles of SO3 = -x Change in moles of SO2 = +x Change in moles of O2 = +(x/2) Given that at equilibrium, 3.0 moles of SO2 is present, we can find the change in moles ('x') for SO2. x = final moles of SO2 - initial moles of SO2 x = 3.0 - 0 x = 3.0 Now we can use the above values to find the changes in moles for SO3 and O2. Change in moles of SO3 = -x = -3.0 Change in moles of O2 = +(x/2) = +(3.0/2) = +1.5 #Step 2: Determine the equilibrium moles for each gas in the reaction#

Now we can calculate the equilibrium moles for each gas using the change in moles we've just found. Equilibrium moles of SO3 = initial moles of SO3 + change in moles of SO3 = 12.0 - 3.0 = 9.0 Equilibrium moles of SO2 = initial moles of SO2 + change in moles of SO2 = 0 + 3.0 = 3.0 Equilibrium moles of O2 = initial moles of O2 + change in moles of O2 = 0 + 1.5 = 1.5 #Step 3: Calculate the equilibrium concentrations for each gas in the reaction#

To calculate the equilibrium constant, we need to find the equilibrium concentrations of the gases involved in the reaction. We can use the total volume of the container (3.0 L) and the equilibrium moles we've just found to calculate the equilibrium concentrations. Equilibrium concentration of SO3 = equilibrium moles of SO3 / total volume = 9.0 moles / 3.0 L = 3.0 M Equilibrium concentration of SO2 = equilibrium moles of SO2 / total volume = 3.0 moles / 3.0 L = 1.0 M Equilibrium concentration of O2 = equilibrium moles of O2 / total volume = 1.5 moles / 3.0 L = 0.5 M #Step 4: Calculate the equilibrium constant (K) for the reaction#

Now we can use the equilibrium concentrations of the gases to calculate the equilibrium constant (K) for the reaction. We will use the expression for K as follows: $K = \frac{[SO2]^2[O2]}{[SO3]^2}$ Plugging in the equilibrium concentrations: $K = \frac{(1.0)^2(0.5)}{(3.0)^2} = \frac{0.5}{9.0} = 0.056$ So the equilibrium constant (K) for this reaction is 0.056.