Q.For the reaction $2NH_3 \rightarrow N_2 + 3H_2$, if $-\dfrac{d[NH_3]}{dt}=k_1[NH_3]$, $\dfrac{d[N_2]}{dt}=k_2[NH_3]$, $\dfrac{d[H_2]}{dt}=k_3[NH_3]$ then the relation between $k_1,k_2$ and $k_3$ is

Using the balanced equation $2H_2O_2\rightarrow 2H_2O+O_2$, the rate of $O_2$ formation is found from the given mass, and the rate of water formation is twice that (since $H_2O$ and $H_2O_2$ share the coefficient 2, while $O_2$ has coefficient 1).

For the reaction $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$, the rate of reaction is expressed uniformly across all species using their stoichiometric coefficients: $\text{Rate} = -\dfrac{1}{2}\dfrac{d[H_2O_2]}{dt} = \dfrac{1}{2}\dfrac{d[H_2O]}{dt} = \dfrac{d[O_2]}{dt}$

Step 1 — rate of $O_2$ formation: $48\ g$ of $O_2$ forms per minute. Molar mass of $O_2 = 32\ g\,mol^{-1}$, so $\dfrac{d[O_2]}{dt} = \dfrac{48}{32} = 1.5\ mol\,min^{-1}$

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mol dm^-3 s^-1 is a unit of concentration divided by time, which matches the definition of reaction rate.

The rate of a reaction is defined as the change in concentration of a reactant or product per unit time, so its unit is (concentration unit)/(time unit) = mol dm^-3 s^-1. This is distinct from: 'order' of reaction, which is a dimensionless number (the sum of the powers of concentration terms in the rate law); 'active mass', which is simply the molar concentration itself (mol dm^-3, no time term); and the 'rate constant' k, whose unit varies with the order of the reaction (e. …