Kp for the reaction CO2(g) + C(s) 2CO(g) is 1.47 at 727°C. Calculate Kc at this temperature

Answer A. 0.0179
B. 0.0246
C. 121
D. 87.7
E. 1.47

To calculate Kc at a given temperature, you need to use the relationship between Kp and Kc, which is given by the following equation:

Kp = Kc(RT)^(Δn)

Where:
- Kp is the equilibrium constant expressed in terms of partial pressures
- Kc is the equilibrium constant expressed in terms of molar concentrations
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
- Δn is the difference in the number of moles between the products and the reactants

In this case, the reaction is CO2(g) + C(s) → 2CO(g), and we need to calculate Kc at 727°C.

First, let's determine the value of Δn. We can do this by comparing the number of moles of the products to the number of moles of the reactants.

For the reactants:
- CO2: 1 mole
- C: 1 mole

For the products:
- CO: 2 moles

Δn = (2 - 1 - 1) = 0

Now, we can plug the values into the equation:

Kp = Kc(RT)^(Δn)

Since the question mentions that Kp = 1.47 at 727°C, we can substitute the values:

1.47 = Kc(0.0821 L·atm/(mol·K))^(0)

Simplifying:

1.47 = Kc(0.0821)

Now, divide both sides by 0.0821:

Kc = 1.47 / 0.0821

Kc ≈ 17.93

Therefore, the correct answer is A. 0.0179.

To calculate Kc at a given temperature, we need to use the equation:

Kc = Kp(RT)^(∆n)

Where:
- Kc is the equilibrium constant at the given temperature
- Kp is the equilibrium constant in terms of partial pressures
- R is the gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
- ∆n is the change in the number of moles of gas from reactants to products

In this case, we have:

CO2(g) + C(s) ⇌ 2CO(g)

∆n = (number of moles of gas on the product side) - (number of moles of gas on the reactant side)
= (2) - (1 + 0)
= 1

Now we can substitute the values into the equation to calculate Kc:

Kc = Kp(RT)^(∆n)
= 1.47(0.0821)(727+273)^(1)
= 1.47(0.0821)(1000)
= 0.121

Therefore, the value of Kc at 727°C is 0.121.

The correct answer is C) 0.121.

Kp = Kc(RT)^delta n