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Reactions with kp and kc

For the reaction
N2(g)+3h2(g) =2NH3(g)
The partial pressure of N2 and H2 are 0.80 and 0.40 atmosphere respectively at equilibrium. The
total pressure of the system is 2.80 atm at 100 oC. What is Kp and Kc for the above reaction?
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1 Answer

Hi again,
 
The equilibrium constant expressed using the partial pressures of gases is Kp. It works exactly like Kc, except we use partial pressure instead of concentration. Kp = [partial pressure of products]^m / [partial pressure of reactants]^n, where m and n are stoichiometric coefficients. In this problem,
 
N2 + 3 H2 -> 2 NH3
 
so Kp = [NH3]^2 / [N2][H2]^3
 
We know the partial pressure of nitrogen and hydrogen, and we also know the total pressure. The sum of all the partial pressures is equal to the total pressure, so we can use this to find the partial pressure of ammonia. 0.80atm + 0.40atm = 1.20atm, and 2.80atm - 1.20atm = 1.60atm. This is the partial pressure of NH3. We can solve for Kp by substituting these values into our earlier expression. This is left as an exercise to the reader.
 
For Kc, we know that the following relation is true:
 
Kp = Kc*(RT)^deltaN
 
where R is the gas constant, T is the temperature, and deltaN is the change in the number of moles of gas. To calculate deltaN, use moles of products - moles of reactants. In our reaction,
 
N2 + 3 H2 -> 2 NH3
 
there are two moles of products and four moles of reactants, so deltaN is -2. The gas constant is 0.0821 L*atm / mol*K, and the temperature is 373 Kelvin. Make sure that you use the absolute temperature in Kelvin, and not the temperature in °C for this calculation. Rearrange your equation, and solve for Kc!

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