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

`K=K_1K_2^2`

Step-by-step 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=([NO]^4[H_2O]^6)/([NH_3]^4[O_2]^5)\\ \\K_2=([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)=([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=([NO]^4[H_2O]^6)/([NH_3]^4[O_2]^5)*([NO_2]^4)/([NO]^4[O_2]^2)=([H_2O]^6[NO_2]^4)/([NH_3]^4[O_2]^7)`

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

`K=([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.