Question

Consider the chemical reaction, $N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$. The rate of this reaction can be expressed in terms of time derivative of concentration of $N_2\left(g\right),H_2$ or $N{H}_3\left(g\right)$. Identify the correct relationship amongst the rate expressions.

• A. Rate $=\frac{-d\left[N_2\right]}{dt}=\frac{-1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
• B. Rate $=\frac{-d\left[N_2\right]}{dt}=-3\frac{d\left[H_2\right]}{dt}=2\frac{d\left[N{H}_3\right]}{dt}$
• C. Rate $=\frac{-d\left[N_2\right]}{dt}=\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
• D. Rate $=\frac{-d\left[N_2\right]}{dt}=\frac{d\left[H_2\right]}{dt}=\frac{d\left[N{H}_3\right]}{dt}$

Answer 1

The correct option is A Rate $=\frac{-d\left[N_2\right]}{dt}=\frac{-1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$

The reaction rate is expressed as a derivative of the concentration of reactant $A$ or product $C$, with respect to time, $t$:

$rate=\underset{\Delta t\to 0}{lim}\frac{-\Delta \left[A\right]}{\Delta t}=\frac{-d\left[A\right]}{dt}$ or $\underset{\Delta t\to 0}{lim}\frac{\Delta \left[C\right]}{\Delta t}=\frac{d\left[C\right]}{dt}$

For reaction

$N_2+3H_2\to 2N{H}_3$

Rate $=\frac{-d\left[N_2\right]}{dt}=\frac{-1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$