Question:
$\text{On increasing the pressure, the direction in which the gas phase reaction proceeds to re-establish equilibrium is predicted by applying Le-Chatelier's principle. Consider the reaction,}$
$\text{N}_2\text{(g)} + \text{3H}_2\text{(g)} \rightleftharpoons \text{2NH}_3\text{(g)}$
$\text{Which of the following is correct, if the total pressure at which the equilibrium is established is increased without changing the temperature?}$
Solution:
$\text{Hint: K is only temperature dependent.}$
$\text{Explanation:}$
$\text{Let's analyze this question carefully:}$
$\text{1. The equilibrium constant K for a reaction is a function of temperature only. It does not change with pressure, concentration, or the addition of a catalyst.}$
$\text{2. While pressure changes can shift the position of equilibrium (i.e., the relative amounts of reactants and products), they do not change the value of the equilibrium constant K itself.}$
$\text{3. When pressure increases, according to Le Chatelier's principle, the reaction will shift to favor the side with fewer moles of gas:}$
$\text{N}_2\text{(g)} + \text{3H}_2\text{(g)} \rightleftharpoons \text{2NH}_3\text{(g)}$
$\text{Left side: 4 moles of gas (1 mole of N}_2 \text{ and 3 moles of H}_2\text{)}$
$\text{Right side: 2 moles of gas (2 moles of NH}_3\text{)}$
$\text{So increasing pressure will shift the equilibrium toward the right (product side) because there are fewer moles of gas on that side. This will increase the concentration of NH}_3 \text{ and decrease the concentrations of N}_2 \text{ and H}_2\text{.}$
$\text{4. However, this shift in equilibrium does not change the value of K. The equilibrium constant K depends only on temperature.}$
$\text{Therefore, even though increasing pressure will shift the position of this equilibrium toward the products (right side), the value of the equilibrium constant K will remain the same as long as the temperature is constant.}$
$\text{The correct answer is option 1: K will remain the same.}$