Given the reaction below
2NOBr(g) <==> 2NO(g) + Br2(g)
and the value of Kc = 1.98, at a temperature of 480 K what is the value of Kp ?
(Hint: Use the value of R in the appropriate units.)
I used the equation Kp=Kc(RT)^Delta N
Then plugged in to get Kp=1.98(.0821x480k)^-1
I get the answer 5.02E-2
what am I doing wrong, and how do I do this correctly?
You started right but went wrong when you calculated delta n.
delta n = (nproducts)-(nreactants) = 3-2 = 1 and not -1.
Oh! Thank you :)
To obtain the correct value of Kp, you need to correct your calculation of the reaction quotient Q in terms of partial pressures. Then, you can use the relationship between Kp and Kc to find the value of Kp.
First, let's calculate the reaction quotient Q in terms of partial pressures. Q is calculated in the same way as Kc, but using the actual partial pressures of the reaction components rather than their equilibrium concentrations:
Qp = (P(NO)^2 * P(Br2)) / (P(NOBr)^2)
Now, since we know that Kp = Qp at equilibrium, we can substitute the given value of Kc and solve for Qp:
1.98 = (P(NO)^2 * P(Br2)) / (P(NOBr)^2) (Equation 1)
Next, we need to consider the relationship between pressure and concentration for gases. According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
To relate partial pressure and molar concentration, we use the equation:
P = nRT / V
Since the volume and temperature remain constant, we can rewrite this equation as:
P = (constant) * n
Now, substituting the partial pressure terms in Equation 1 with their respective molar concentration terms, we have:
1.98 = (([NO]^2 / V^2) * ([Br2] / V)) / ([NOBr]^2 / V^2)
We can simplify this to:
1.98 = ([NO]^2 * [Br2]) / [NOBr]^2 (Equation 2)
Now, we need to relate the concentrations to the equilibrium constant Kp using the equation:
Kp = (P(NO)^2 * P(Br2)) / (P(NOBr)^2)
Using the same reasoning as before, we can write:
Kp = ([NO]^2 * [Br2]) / [NOBr]^2 (Equation 3)
Comparing Equations 2 and 3, we see that they are the same. This means that Kp = Kc, and there is no need to convert Kc to Kp using the ideal gas law.
Hence, the correct value of Kp is 1.98.