The eThe equilibrium constant for the reaction CO(g) + H2O(g) ⇔ CO2(g) + H2(g) is 3 at 500º C.In a 2 litre vessel 60 g of water gad and 90 g steam . Find the number of moles of H2 at equilibrium

To find the number of moles of H2 at equilibrium for the reaction CO(g) + H2O(g) ⇔ CO2(g) + H2(g), we need to start by determining the initial amounts of each substance involved in the reaction. We can then apply the equilibrium constant to find the equilibrium concentrations and ultimately the moles of H2.

Step 1: Calculate Initial Moles

First, we need to convert the masses of water and steam into moles. The molar mass of water (H2O) is approximately 18 g/mol.

• For water (60 g):

  Number of moles = mass / molar mass = 60 g / 18 g/mol = 3.33 moles

• For steam (90 g):

  Number of moles = mass / molar mass = 90 g / 18 g/mol = 5 moles

Step 2: Set Up the Reaction Table

Next, we can set up an ICE (Initial, Change, Equilibrium) table to track the changes in moles as the reaction reaches equilibrium.

Step 3: Apply the Equilibrium Constant

The equilibrium constant (K) for the reaction is given as 3 at 500º C. The expression for the equilibrium constant is:

K = [CO2][H2] / [CO][H2O]

Substituting the equilibrium concentrations into the expression, we have:

3 = (x)(x) / (x)(8.33 - x)

Step 4: Solve for x

Rearranging the equation gives:

3 = x² / (x(8.33 - x))

Multiplying both sides by (x(8.33 - x)) results in:

3x(8.33 - x) = x²

Expanding this gives:

24.99x - 3x² = x²

Combining like terms leads to:

4x² - 24.99x = 0

Factoring out x gives:

x(4x - 24.99) = 0

This results in two solutions: x = 0 or x = 6.2475. Since x cannot be zero in this context, we take x = 6.2475.

Step 5: Calculate Moles of H2

At equilibrium, the number of moles of H2 is equal to x, which we found to be approximately 6.25 moles. Therefore, the number of moles of H2 at equilibrium is:

6.25 moles

In summary, by calculating the initial moles, setting up an ICE table, applying the equilibrium constant, and solving for x, we determined that there are about 6.25 moles of H2 present at equilibrium in the reaction.