The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N₂(g) + O₂(g) 2NO(g)
At 2000.°C,the equilibrium constant,K_c,has a value of 4.10 × 10^-4.What is the value of K_P?
(R = 0.08206 L • atm/K • mol)

Question

The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N₂(g) + O₂(g)

The reaction of nitrogen with oxygen to form nitrogen monoxide can be represented by the following equation. N<sub>2</sub>(g) + O<sub>2</sub>(g) 2NO(g) At 2000.°C,the equilibrium constant,K<sub>c</sub>,has a value of 4.10 × 10<sup>-4</sup>.What is the value of K<sub>P</sub>? (R = 0.08206 L • atm/K • mol) A) 2.17 × 10<sup>-8</sup> B) 4.10 × 10<sup>-4</sup> C) 7.65 × 10<sup>-2</sup> D) 2.20 ×10<sup>-6</sup> E) 2.44 ×10<sup>3</sup>

2NO(g)
At 2000.°C,the equilibrium constant,K_c,has a value of 4.10 × 10^-4.What is the value of K_P?
(R = 0.08206 L • atm/K • mol)

Quizplus · Accepted Answer

The equilibrium constant, $K_c$, is given by:
$$K_c=\frac{[NO]^2}{[N_2][O_2]}$$
Taking the natural logarithm of both sides, we get:
$$\ln K_c=\ln\left(\frac{[NO]^2}{[N_2][O_2]}ight)=2\ln[NO]-\ln[N_2]-\ln[O_2]$$
Using the ideal gas law, we can relate the concentrations to the partial pressures:
$$\ln K_p=\ln\left(\frac{P_{NO}^2}{P_{N_2}\cdot P_{O_2}}ight)=2\ln P_{NO}-\ln P_{N_2}-\ln P_{O_2}$$
At 2000°C, the conversion factor between $K_c$ and $K_p$ is:
$$K_p=K_c(RT)^{\Delta n}$$
where $\Delta n$ is the difference between the sum of the stoichiometric coefficients of the gaseous products and the sum of the stoichiometric coefficients of the gaseous reactants. In this case, we have $\Delta n=2-1-1=0$.
Substituting the values given in the problem, we get:
$$\ln K_p=\ln\left(\frac{P_{NO}^2}{P_{N_2}\cdot P_{O_2}}ight)=\ln K_c+\ln(RT)^{\Delta n}=\ln K_c$$
Therefore,
$$\ln K_p=-4\ln 10+\ln 4.10=-8.09$$
Taking the antilogarithm of both sides, we get:
$$K_p=3.94	imes 10^{-9}$$
which is closest to option B.

The Reaction of Nitrogen with Oxygen to Form Nitrogen Monoxide