Express the equilibrium constant for the following reaction.

3 P4(s) + 15 O2(g) 3 P4O10(s)

Question

Express the equilibrium constant for the following reaction.

3 P4(s) + 15 O2(g)  3 P4O10(s)

BlackTom AI · Accepted Answer

The reaction given is: 3 P4(s) + 15 O2(g) ⇌ 3 P4O10(s).

First, recall the general form of the equilibrium constant expression: K = (activities of products) / (activities of reactants).

Next, identify which species are in the gas phase and which are solids. Oxygen (O2) is a gas, while the phosphorus-containing species P4(s) and P4O10(s) are solids.

For solids, the activity is taken as 1 (they do not appear in the expression with a pressure or concentration term).

Therefore, in the numerator we would have the activity of the solid product P4O10, which is 1, raised to its stoichiometric coefficient. Since 3 P4O10(s) are formed, the product term contributes 1 altogether because (1)^3 = 1.

In the denominator, we have the activities of the reactants. P4(s) has activity 1, and O2(g) has an activity equal to its partial pressure P_O2 (in the standard form, use Kp or Kc consistently; here we consider the same idea with partial pressure for gases). The coefficient 15 on O2 in the balanced equation means P_O2 is raised to the 15th power: (P_O2)^{15}.

Putting it together, the equilibrium expression becomes K = (1) / [(1)^3 · (P_O2)^{15}] = 1 / (P_O2)^{15}.

If the context requires Kp rather than K, the same logic applies because the gas component is described by partial pressure; the expression would still involve P_O2 to the 15th power in the denominator.

Important nuance: since the products are solids, their activities are effectively constant and do not influence the numerical value of K; only the gas-phase reactants (O2) determine the K value in this case.

If you were given multiple-choice options, you would look for an option that expresses K as 1 divided by P_O2 raised to the 15th power, reflecting the 15 O2(g) in the reactant side and the presence of only solids in both product and remaining reactants.

Express the equilibrium constant for the following reaction. 3 P4(s) + 15 O2(g) 3 P4O10(s)

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