The equilibrium constant, Kp, for the following reaction is 2.74 at 1150 K.
Calculate Kc for this reaction at this temperature.
2SO3(g) 2SO2(g) + O2(g)
Kp = Kc(RT)^delta n.
To calculate Kc for this reaction at the given temperature, you need to first convert the value of Kp to Kc using the ideal gas law. The ideal gas law states that the relationship between the pressure and concentration of gases is given by the equation:
Kc = Kp * (RT)^Δn
Where:
Kc is the equilibrium constant in terms of concentrations (mol/L)
Kp is the equilibrium constant in terms of partial pressures (atm)
R is the gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin (K)
Δn is the difference in the number of moles of gaseous products and reactants
In the given reaction:
2SO3(g) 2SO2(g) + O2(g)
The difference in the number of moles of gaseous products and reactants (Δn) is:
(2+1) - (2) = 1
Now you can calculate Kc using the equation mentioned above:
Kc = Kp * (RT)^Δn
Kp = 2.74 (given)
R = 0.0821 L·atm/mol·K (gas constant)
T = 1150 K (temperature)
Δn = 1 (difference in moles of products and reactants)
Substituting the values into the equation:
Kc = 2.74 * (0.0821 L·atm/mol·K * 1150 K)^1
Now, calculate (0.0821 L·atm/mol·K * 1150 K)^1:
0.0821 * 1150 = 94.365
Kc = 2.74 * 94.365^1
Therefore, Kc = 2.74 * 94.365 = 257.983
So, the value of Kc for the given reaction at 1150 K is approximately 257.983.