How Do Coefficient Changes Affect Equilibrium Constants?

[Johnyi]

Homework Statement

The reaction below has a equilibrium constant of Kp = 2.26 x 10^4 at 298 K
CO(g) + 2H2(g) <=>CH3OH(g)

Calculate Kp for each of the reactions and predict whether reactants or products will be favored at equilibrium

A. (1/2)CO(g) + H2(g) <=> (1/2)CH3OH(g)

Homework Equations

The Attempt at a Solution

I know i have to multiply all the coefficients by something..but i just don't know by what. How can i tell?

 

[Borek]

Write both reaction quotients and see how they are related.

 

[Johnyi]

Write both reaction quotients and see how they are related.

Im not sure what you mean by this. Can you explain more please

 

[Borek]

Write formulas for equilibrium constants and see if there is no some simple operation that can convert one into the other.

 

[DeeNos]

As a scientist, your first step should be to identify the given information and determine what is being asked for. In this case, the given information is the equilibrium constant (Kp = 2.26 x 10^4) and the reaction (CO(g) + 2H2(g) <=> CH3OH(g)). The question is asking for the equilibrium constant for a modified reaction (1/2)CO(g) + H2(g) <=> (1/2)CH3OH(g)) and to predict whether reactants or products will be favored at equilibrium.

To solve this problem, you will need to use the equilibrium constant expression, Kp = [CH3OH]^1/[CO]^1

^2, where the coefficients represent the stoichiometric coefficients of the reactants and products in the balanced equation. In this case, the coefficients for CO and H2 are 1 and for CH3OH is 1.

To calculate the equilibrium constant for the modified reaction, you will need to use the coefficients given in the modified reaction (1/2)CO(g) + H2(g) <=> (1/2)CH3OH(g)). This means that the new equilibrium constant will be Kp = [(1/2)CH3OH]^1/[(1/2)CO]^1

^2. Simplifying this expression, we get Kp = [CH3OH]^1/[CO]^1

^2. This is the same equilibrium constant expression as the original reaction, meaning that the equilibrium constant for the modified reaction will also be Kp = 2.26 x 10^4.

To predict whether reactants or products will be favored at equilibrium, we can compare the magnitude of the equilibrium constant to the value of 1. If the equilibrium constant is greater than 1, products will be favored at equilibrium. If the equilibrium constant is less than 1, reactants will be favored at equilibrium. In this case, the equilibrium constant is much greater than 1 (2.26 x 10^4 >> 1), so products will be favored at equilibrium.

In summary, the equilibrium constant for the modified reaction is Kp = 2.26 x 10^4 and products will be favored at equilibrium.