The order of a reaction refers to the mathematical expression that describes how the rate of a chemical reaction changes with respect to the concentration of reactants. It is determined experimentally and may or may not correspond to the stoichiometric coefficients in the balanced chemical equation of the reaction.

In a general form, for a reaction:

aA+bB→cC+dDaA+bB→cC+dD

where AA, BB, CC, and DD are reactants or products, and aa, bb, cc, and dd are their respective stoichiometric coefficients, the rate of the reaction can be expressed as:

Rate=k[A]m[B]nRate=k[A]m[B]n

where:

• kk is the rate constant,
• [A][A] and [B][B] are the concentrations of reactants A and B, respectively,
• mm and nn are the order of reaction with respect to A and B, respectively.

The overall order of the reaction is the sum of the individual orders (m+nm+n). The orders can be zero, first, second, etc., and they represent how the rate of the reaction is influenced by changes in the concentration of reactants. Determining the order of a reaction is crucial for understanding its kinetics and designing reaction mechanisms.

The rate of the reaction can be expressed in terms of the formation of ammonia (NH3) by considering the change in the concentration of NH3 over time. According to the balanced equation:

N2(g)+3H2(g)→2NH3(g)N2(g)+3H2(g)→2NH3(g)

The rate of formation of NH3 can be expressed as:

Rate=−12Δ[NH3]ΔtRate=−21ΔtΔ[NH3]

This negative sign indicates that the concentration of NH3 decreases over time as it is consumed in the reaction. The coefficient 1221 in front of Δ[NH3]ΔtΔtΔ[NH3] is there to ensure that the rate is expressed per mole of NH3 formed.

Now, according to the stoichiometry of the reaction, 1 mole of N2 and 3 moles of H2 are required to produce 2 moles of NH3. Therefore, the rate of formation of NH3 can also be expressed in terms of the reactants:

Rate=12(−Δ[N2]Δt)=16(−Δ[H2]Δt)Rate=21(−ΔtΔ[N2])=61(−ΔtΔ[H2])

This equation shows how the rate of formation of NH3 relates to the rates of disappearance of N2 and H2.

The order of a reaction can be determined by examining the units of the rate constant kk.

For a reaction with rate constant kk expressed in units of s−1s−1, the reaction is said to be first order.

So, given that k=3×10−4 s−1k=3×10−4s−1, the reaction is first order.