Methane reacts with water to form CO and H2 as follows: CH4(g)+H2O(g)=CO9g)+3H2(g) The value of Kp at 298 k for the reaction is 7.7 *10^24, calculate Kc. If you can please show the steps I would greatly appreciate it. Thank you

1.3 x 10^22

Kp = Kc(RT)^delta n.

delta n = product mols - reactant mols = 4-2 = 2
7.7E24 = Kc(0.08206*298)^2
Kc = ?

To calculate the value of Kc, we need to relate it to the value of Kp using the ideal gas law equation:

Kp = Kc(RT)^(Δn)

Where:
Kp is the equilibrium constant in terms of pressure
Kc is the equilibrium constant in terms of concentration
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
Δn is the change in the number of moles of gas

In this case, we can determine Δn by using the stoichiometric coefficients of the balanced equation:
CH4(g) + H2O(g) → CO(g) + 3H2(g)

Δn = (1+0) - (1+3) = -3

Now, let's plug in the given values into the equation:

Kp = Kc(RT)^(Δn)

Kp = 7.7 * 10^24
R = 0.0821 L·atm/mol·K
T = 298 K
Δn = -3

Kc = Kp / (RT)^(Δn)

Kc = (7.7 * 10^24) / (0.0821 L·atm/mol·K * 298 K)^(-3)

Kc = (7.7 * 10^24) / (0.0821 * 298)^(-3)

Kc ≈ 1.6 * 10^30

Therefore, the value of Kc is approximately 1.6 * 10^30.

To calculate Kc from Kp, we need to use the equation relating these two equilibrium constants for gaseous reactions:

Kp = Kc(RT)^(Δn)

Where:
- Kp is the equilibrium constant based on the partial pressure of the reactants and products.
- Kc is the equilibrium constant based on the molar concentrations of the reactants and products.
- R is the ideal gas constant (0.0821 L.atm/mol.K).
- T is the temperature in Kelvin.
- Δn is the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.

In this case, we are given Kp and we need to find Kc. Let's determine Δn first.

Reactants:
CH4(g) + H2O(g)

Products:
CO(g) + 3H2(g)

Reactant moles:
1 mol of CH4 and 1 mol of H2O

Product moles:
1 mol of CO and 3 mol of H2

Δn = (moles of products) - (moles of reactants)
= (1 + 3) - (1 + 1)
= 3 - 2
= 1

Now we can substitute Δn, R, and the given temperature into the formula:

Kp = Kc(RT)^(Δn)

Kp = 7.7 * 10^24
R = 0.0821 L.atm/mol.K
T = 298 K
Δn = 1

Kp = Kc * (0.0821 L.atm/mol.K * 298 K)^(1)

Simplifying:

7.7 * 10^24 = Kc * (24.4258)

Dividing both sides by 24.4258:

Kc = (7.7 * 10^24) / (24.4258)

Kc ≈ 3.15 * 10^23

Therefore, Kc ≈ 3.15 * 10^23.