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.