Question

For which of the following reactions is the ratio kp/kc largest at 300 k?

Answer 1

Answer:

Reaction c. has the largest value of $\frac{k_{p} }{k_{c} } = 1.55 X 10^{10}$ at 300 K

Explanation:

Here is the complete question

Converting between Kc and Kp For which of the following reactions is the ratio Kp/Kc largest at 300 K?  

a. N2(g) + O2(g) ⇌ 2 NO(g)

b. C(s) +2H2(g) ⇌ CH4(g)

c. Ni(CO)4(g) ⇌ Ni(s) + 4CO(g)

d. CaCO3(s) ⇌ CaO(s) + CO2(g)

Solution

$k_{p} = k_{c}(RT)^{n}\\\frac{k_{p} }{k_{c} } = (RT)^{n}$

where R = molar gas constant = 8.314 J/mol-K, T = temperature = 300 K and n = number of moles of products - number of moles of reactants

For reaction a. number of moles of gaseous products = 2, number of moles of gaseous reactants = 2. So n = 2 - 2 = 0

So, $\frac{k_{p} }{k_{c} } = (RT)^{n} = (RT)^{0} = 1$

For reaction b. number of moles of gaseous products = 1, number of moles of gaseous reactants = 2. So n = 1 - 2 = -1 (we do not include the solid)

So, $\frac{k_{p} }{k_{c} } = (RT)^{n} = (RT)^{-1} = (8.314 X 300)^{-1} = (2494.2)^{-1} = 4.01 X 10^{-4}$

For reaction c. number of moles of gaseous products = 5, number of moles of gaseous reactants = 1. So n = 4 - 1 = 3 (we do not include the solid)

So, $\frac{k_{p} }{k_{c} } = (RT)^{n} = (RT)^{3} = (8.314 X 300)^{3} = (2494.2)^{3} = 1.55 X 10^{10}$

For reaction d. number of moles of gaseous products = 2, number of moles of gaseous reactants = 0. So n = 2 - 0 = 2 (we do not include the solid)

So, $\frac{k_{p} }{k_{c} } = (RT)^{n} = (RT)^{2} = (8.314 X 300)^{2} = (2494.2)^{2} = 6.22 X 10^{6}$

Since $\frac{k_{p} }{k_{c} } = 1.55 X 10^{10}$ for reaction c which is the largest value. So, reaction c. has the largest value of $\frac{k_{p} }{k_{c} } = 1.55 X 10^{10}$ at 300 K

Answer 2

Below are the choices:

A. Ni(CO)4(g) ⇌ Ni(s) + 4CO(g)
B. C(s) +2H2(g) ⇌ CH4(g)
C. CaCO3(s) ⇌ CaO(s) + CO2(g)
D. N2(g) + O2(g) ⇌ 2 NO(g)

The answer is A. Ni(CO)4(g) ⇌ Ni(s) + 4CO(g)

The Kp/Kc ratio is equal to (RT)Δn. K is a constant and the temperature is held constant. So, the Kp/Kc ratio depends on Δn or the difference of moles of gaseous product and reactant. The reaction with the greatest Kp/Kc ratio is Ni(CO)4(g) ⇌ Ni(s) + 4CO(g) with a Δn of 3.