Writing Relative Rate Expressions from a Balanced Equation
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Writing a reaction's relative rate expressions means dividing each substance's concentration-change rate by its own stoichiometric coefficient, with reactant rates carrying a negative sign so every resulting term equals the same positive overall rate.
For the combustion of ammonia, 4 NH3 + 5 O2 → 4 NO + 6 H2O, the overall rate equals −(1/4)Δ[NH3]/Δt, equals −(1/5)Δ[O2]/Δt, equals (1/4)Δ[NO]/Δt, equals (1/6)Δ[H2O]/Δt. If oxygen is consumed at 2.0 × 10⁻⁴ mol/L/s, dividing by its coefficient of 5 gives an overall rate of 4.0 × 10⁻⁵ mol/L/s; multiplying that overall rate by water's coefficient of 6 gives water's formation rate, 2.4 × 10⁻⁴ mol/L/s.
Forgetting the negative sign on a reactant's term, or dividing by the wrong substance's coefficient, produces a rate expression that does not equal the same value as every other substance's term in the reaction.
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