Question

Consider a mixture of \(\mathrm{CO}_{2}, \mathrm{CO},\) and \(\mathrm{O}_{2}\) in equilibrium at a specified temperature and pressure. Now the pressure is doubled. (a) Will the equilibrium constant \(K_{P}\) change? (b) Will the number of moles of \(\mathrm{CO}_{2}\), \(\mathrm{CO}\), and \(\mathrm{O}_{2}\) change? How?

Short answer

If so, in what way? Answer: The equilibrium constant will not change when the pressure is doubled. However, the number of moles of CO2, CO, and O2 will change. The moles of CO2 will decrease, while the moles of CO and O2 will increase.

Step-by-step solution

Part (a) - Will the equilibrium constant \(K_P\) change?

The equilibrium constant (\(K_P\)) is affected only by changes in temperature. In this exercise, we are told that the temperature remains constant while the pressure is doubled. As a result, the equilibrium constant \(K_P\) will remain unchanged. Part (a) Answer: No, the equilibrium constant \(K_P\) will not change.

Part (b) - Will the number of moles of CO2, CO, and O2 change?

To answer this part, let's consider the following reaction equation which states the formation of CO2, CO and O2: \(\mathrm{CO}_{2} \leftrightarrows \mathrm{CO} + \frac{1}{2} \mathrm{O}_{2}\) When the pressure is doubled, the system will attempt to counteract the change and re-establish the equilibrium. According to Le Chatelier's principle, if a system in equilibrium is subjected to a change in pressure, the equilibrium will shift in the direction that results in a change in the number of moles that counteracts the applied change. In this case, doubling the pressure results in the system shifting to the side with fewer moles of gas (in the direction where the pressure is partially reduced). The forward reaction produces fewer moles of gaseous products (1 mole of CO and half a mole of O2) compared to the reverse reaction that produces one mole of CO2. Thus, the equilibrium will shift to the right (favoring the forward reaction) upon doubling the pressure. This will result in an increase in the moles of CO and O2 and a decrease in the moles of CO2. Part (b) Answer: Yes, the number of moles of CO2, CO, and O2 will change. The moles of CO2 will decrease, while the moles of CO and O2 will increase.