Calculating the equilibrium composition by approximation

[makaela2L]

Self-Test 5I.3A: The initial partial pressures of nitrogen and hydrogen in a rigid, sealed vessel are 0.010 and 0.020 bar, respectively. The mixture is heated to a temperature at which K=0.11 for N2(g) + 3 H2(g) <---> 2 NH3(g). What are the equilibrium partial pressures of each substance in the reaction mixture?

May someone please explain why would we approximate in this problem? Because I thought we only use approximation if K < .

Edit: For clarification, the textbook had this question within the section titled: "Calculating the equilibrium composition by approximation."
And the answers were N2=0.010, H2=0.020, and NH3= 9.4 x 10^-5

[Emily_Haywood_1K]

The threshold for approximation is 10^-3, therefore in this problem you would not be able to approximate. You must solve the entire quadratic equation.

[Luka Gogorishvili 1K]

In this problem, K=0.11. This would be the same as 1.1*10^-1. Because this value is not as small as, for example, 1.1*10^-3, you would have to carry out the full calculation.

[Luka Gogorishvili 1K]

Also, you can multiply your K value by 1000 and see if it equals your initial concentration of reactant. If it does, you have to do the full calculation but if not, you can then approximate. This is info taken from the homework hints.

[Jess Kosz 1B]

This problem doesn’t allow for approximation (for an accurate answer) because the equilibrium constant is not smaller than the threshold k is less than 10^-3. In any case where k is greater than 10^-3, then we can use approximation to avoid using the quadratic formula, but since k=0.11, using approximation will yield an incorrect answer!

[Nishanth Vemuri 2L]

Since the K value given in this problem is 0.11, which is greater than 10^-3, we cannot use approximation for this problem and must proceed with the quadratic formula. From here, we can set up an ICE table to find the equilibrium partial pressures of reactants/products in the system, use the equilibrium expression and solve for x. From there, you can find the final pressures!

[Titania Le [2F]]

I was wondering the same thing because for 5H.13, the Kc value was 10^-7. I am confused as to why the solutions manual still required us to solve it through.