Final answer:
The equilibrium constant for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g) is found by taking the original equilibrium constant (K=5 for the reaction 3/2 N2(g) + 2H2(g) ⇌ NH3(g)) to the power of 2/3, resulting in approximately 2.924017.
Step-by-step explanation:
The question is asking to determine the equilibrium constant for the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), given that the equilibrium constant for the reaction 3/2 N₂(g) + 2H₂(g) ⇌ NH₃(g) is 5.
The equilibrium constant (K) for a chemical reaction is the ratio of the product of the concentrations of the products raised to the power of their respective coefficients in the balanced equation to the product of the concentrations of the reactants raised to the power of their respective coefficients.
For the given reaction (N₂ + 3H₂ ⇌ 2NH₃), the coefficient for nitrogen is 1, for hydrogen is 3, and for ammonia is 2. The equilibrium constant expression for this reaction is [NH₃]2 / ([N₂] · [H₂]3).
Since the original reaction is 3/2 N₂ + 2H₂ ⇌ NH₃ with K = 5, by multiplying this reaction by 2/3 to obtain the second reaction, the new K can be calculated by taking the original K to the power of 2/3. Therefore, the equilibrium constant for the second reaction (N₂ + 3H₂ ⇌ 2NH₃) is K = 52/3, which is approximately 2.924017.