Question

The first two steps in the industrial synthesis of nitric acid produce nitrogen dioxide from ammonia: The net reaction is: Write an equation that gives the overall equilibrium constant in terms of the equilibrium constants and . If you need to include any physical constants, be sure you use their standard symbols, which you'll find in the ALEKS Calculator.

Answer 1

Answer:

$K=K_1K_2^2$

Explanation:

Hello,

In this case, the first two steps are:

$4NH_3(g)+5O_2(g)\rightleftharpoons 4NO(g)+6H_2O(g)\\\\2NO(g)+O_2(g)\rightleftharpoons 2NO_2(g)$

And the net reaction:

$4NH_3(g)+7O_2(g)\rightleftharpoons 4NO_2(g)+6H_2O(g)$

Thus, each equilibrium constant turn out:

$K_1=\frac{[NO]^4[H_2O]^6}{[NH_3]^4[O_2]^5}\\ \\K_2=\frac{[NO_2]^2}{[NO]^2[O_2]}$

Thus, if we want to obtain the net equation, we must double the second reaction as:

$4NO(g)+2O_2(g)\rightleftharpoons 4NO_2(g)$

Thereby, its equilibrium constant changes:

$K_2^{new}=\frac{[NO_2]^4}{[NO]^4[O_2]^2}$

Becoming a squared version of the original K₂. In such a way, if we multiple the two equilibrium constants:

$K_1*K_2^2=\frac{[NO]^4[H_2O]^6}{[NH_3]^4[O_2]^5}*\frac{[NO_2]^4}{[NO]^4[O_2]^2}=\frac{[H_2O]^6[NO_2]^4}{[NH_3]^4[O_2]^7}$

Next, we express the net reaction equilibrium constant, that is:

$K=\frac{[H_2O]^6[NO_2]^4}{[NH_3]^4[O_2]^7}$

Therefore, K in terms of K₁ and K₂ results:

$K=K_1K_2^2$

Best regards.