Kp < Kc at 25 degrees C for which of the reactions below?
N2 + 3H2 <-----> 2NH3
2NO <------> N2 + O2
C + O2 <------> CO2
2NOCl <-------> 2NO + Cl2
I don't even know where to start. I really want to understand this, not just an answer
You look at the equation for converting Kp to Kc (or Kc to Kp). One of them is as follows:
Kp = Kc(RT)delta n
Therefore, the ONLY difference between Kp and Kc is the (RT)^delta n part. So if delta n is zero; i.e., the same number of mols on each side, then delta n = 0, any number to the zero power is 1 and that would mean the RT term would be 1*Kc and Kp = Kc. So what does that mean? You look for an equation where the number of mols on one side is the same as the number of mols on the other. For example, the first equation has 4 mols on the left and 2 on the right so that one isn't the answer. You can do the others.
That is what I thought also, but my teacher says no. He said the correct answer is the first equation, and I don't understand why. Can you explain further?
Yes, I can explain. Both of us made the same mistake and I wouldn't have noticed it if you hadn't reposted. Reread the question. It is NOT (as I first read it) Kp = Kc (Look at my first response and you can see I am always talking about equal). The question reads Kp < Kc. So you want delta n to be negative value so that Kp = Kc(RT)^-2 = Kc/(RT)^2 = Kc/larger term = smaller Kp. #1 is the only equation with a larger number of mols on the left than the right except for #3. I assume #3 doesn't count because C is a solid So you have 1 mol gas on the right and 1 mol on the left.
To determine whether Kp is less than Kc at 25 degrees Celsius for any of the given reactions, we need to compare the expressions for Kp and Kc.
Kp is the equilibrium constant expressed in terms of the partial pressures of the gases involved in the reaction, while Kc is the equilibrium constant expressed in terms of the concentrations (or molarities) of reactants and products.
To begin, let's write the expression for Kp for each reaction:
1. N2 + 3H2 ⟷ 2NH3
Kp = (P(NH3))^2 / (P(N2) * P(H2))^3
2. 2NO ⟷ N2 + O2
Kp = (P(N2) * P(O2)) / (P(NO))^2
3. C + O2 ⟷ CO2
Kp = P(CO2) / (P(C) * P(O2))
4. 2NOCl ⟷ 2NO + Cl2
Kp = (P(NO)^2 * P(Cl2)) / (P(NOCl))^2
Now, let's find the expressions for Kc for each reaction:
1. N2 + 3H2 ⟷ 2NH3
Kc = [NH3]^2 / [N2]^1 * [H2]^3
2. 2NO ⟷ N2 + O2
Kc = [N2]^1 * [O2]^1 / [NO]^2
3. C + O2 ⟷ CO2
Kc = [CO2]^1 / [C]^1 * [O2]^1
4. 2NOCl ⟷ 2NO + Cl2
Kc = [NO]^2 * [Cl2]^1 / [NOCl]^2
To compare Kp and Kc, we need to consider the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Since Kp is expressed in terms of partial pressures, we can assume that the pressure is proportional to the concentration of the gas.
Therefore, at a constant temperature and volume, we can write:
P = (n/V) * (RT)
Now, let's analyze each reaction:
1. N2 + 3H2 ⟷ 2NH3:
In this reaction, the number of moles of gaseous reactants is greater than the number of moles of gaseous products. Therefore, the pressure term in Kp will be higher than the concentration term in Kc. Hence, Kp > Kc for this reaction at 25 degrees Celsius.
2. 2NO ⟷ N2 + O2:
This reaction has equal moles of reactants and products. Hence, the pressure term and the concentration term in Kp and Kc will be equal. Therefore, Kp = Kc for this reaction at 25 degrees Celsius.
3. C + O2 ⟷ CO2:
This reaction involves a solid (C) and a gas (O2), so the mole fraction of C will be much smaller compared to the mole fraction of O2. As a result, the pressure term in Kp will be significantly smaller than the concentration term in Kc. Hence, Kp < Kc for this reaction at 25 degrees Celsius.
4. 2NOCl ⟷ 2NO + Cl2:
This reaction has the same number of moles of reactants and products. Therefore, the pressure term and the concentration term in Kp and Kc will be equal. Hence, Kp = Kc for this reaction at 25 degrees Celsius.
To summarize:
- For the reaction N2 + 3H2 ⟷ 2NH3, Kp > Kc.
- For the reaction C + O2 ⟷ CO2, Kp < Kc.
- For the other two reactions, Kp = Kc.
Remember, this comparison is specific to 25 degrees Celsius. At different temperatures, the equilibrium constants may differ.