The decomposition of ammonia on a platinum surface is a zero-order reaction: 2 NH ₃( g ) N ₂( g ) + 3 H ₂( g ) If the initial concentration of NH ₃ is 0.5 M and the rate of appearance of H ₂ is 6.0 10⁻³ M min ⁻¹ , what will be the concentration of NH ₃ remaining after 40 minutes?

Step-by-step solution

For the zero-order reaction 2 NH ₃ N ₂ + 3 H ₂ , the rate of reaction is: Rate = - 1 2 d[ NH ₃] dt = 1 3 d[ H ₂] dt = k Given the rate of appearance of H ₂ is 6.0 10⁻³ M min ⁻¹ : d[ H ₂] dt = 3k = 6.0 10⁻³ M min ⁻¹ k = 2.0 10⁻³ M min ⁻¹ The rate of disappearance of NH ₃ is: - d[ NH ₃] dt = 2k = 4.0 10⁻³ M min ⁻¹ Using the integrated rate law for the disappearance of NH ₃ : [ NH ₃]₀ - [ NH ₃]_t = 2kt Substitute the given values ( [ NH ₃]₀ = 0.5 M, t = 40 min): 0.5 - [ NH ₃]_t = (4.0 10⁻³) 40 0.5 - [ NH ₃]_t = 0.16 [