This reaction has an equilibrium constant of K_p = 2.26⨉10⁴ at 298 K. CO(g) + 2 H₂(g) ⇌ CH₃OH(g) Calculate K_p for each reaction and predict whether reactants or products will be favored at equilibrium.
b. 1/2 CO(g) + H₂ (g) ⇌ 1/2 CH₃OH(g)

Verified step by step guidance

1. Step 1: Understand the relationship between the original reaction and the new reaction. In this case, the new reaction is the original reaction divided by 2.
2. Step 2: Use the rule that if a reaction is divided by a factor, the equilibrium constant for the new reaction is the square root of the original equilibrium constant. This is because the equilibrium constant is a ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients. When the coefficients are halved, the powers in the ratio are also halved, which is equivalent to taking the square root.
3. Step 3: Calculate the new equilibrium constant, Kp', by taking the square root of the original Kp. The square root of 2.26⨉10⁴ will give you Kp' for the new reaction.
4. Step 4: Determine whether the reactants or products are favored at equilibrium. If Kp' is greater than 1, the products are favored. If Kp' is less than 1, the reactants are favored.
5. Step 5: Compare the calculated Kp' with 1 to determine whether the reactants or products are favored at equilibrium.

Key Concepts

Equilibrium Constant (Kp)

The equilibrium constant, Kp, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is expressed in terms of partial pressures for gaseous reactions. A larger Kp value indicates that products are favored at equilibrium, while a smaller Kp suggests that reactants are favored.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction, as represented by the balanced equation. It is essential for calculating the equilibrium constant for reactions with different stoichiometric coefficients, as changes in coefficients affect the equilibrium expression and the value of Kp.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions (such as concentration, pressure, or temperature), the system will adjust to counteract the change and restore a new equilibrium. This principle helps predict the direction in which the reaction will shift when the equilibrium is altered, indicating whether reactants or products will be favored.