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Chemistry Question on Chemical Kinetics

Consider the chemical reaction, N2(g)+3H2(g)→2NH3(g)N_2(g)+3H_2(g)\rightarrow 2NH_3(g) .The rate of this reaction can be expressed in terms of time derivatives of concentration of N2(g),H2(g)orNH3(g)N_2(g), H_2(g) or NH_3(g). Identify the correct relationship amongst the rate expressions

A

Rate=−d[N2]dt=−13d[H2]dt=12d[NH3]dtRate=-\frac{d[N_2]}{dt}=-\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}

B

Rate=−d[N2]dt=−3d[H2]dt=2d[NH3]dtRate=-\frac{d[N_2]}{dt}=-3\frac{d[H_2]}{dt}=2\frac{d[NH_3]}{dt}

C

Rate=−d[N2]dt=13d[H2]dt=12d[NH3]dtRate=-\frac{d[N_2]}{dt}=\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}

D

Rate=−d[N2]dt=−d[H2]dt=d[NH3]dtRate=-\frac{d[N_2]}{dt}=-\frac{d[H_2]}{dt}=\frac{d[NH_3]}{dt}

Answer

Rate=−d[N2]dt=−13d[H2]dt=12d[NH3]dtRate=-\frac{d[N_2]}{dt}=-\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}

Explanation

Solution

For any general reaction,
aA+bB→cC+dDaA+bB\rightarrow cC+dD
Rate=−1ad[A]dt=1bd[B]dtRate=-\frac{1}{a}\frac{d[A]}{dt}=\frac{1}{b}\frac{d[B]}{dt}
1cd[C]dt=1dd[D]dt\frac{1}{c}\frac{d[C]}{dt}=\frac{1}{d}\frac{d[D]}{dt}
⇒N2+3H2→2NH3\Rightarrow N_2+3H_2 \rightarrow 2NH_3
Rate=−d[N2]dt=−13d[H2]dt=12d[NH3]dtRate=-\frac{d[N_2]}{dt}=-\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2\frac{d[NH_3]}{dt}}
⇒Rate=k[N2O5]\Rightarrow Rate=k[N_2O_5]
⇒[N2O5]=Ratek=2.40×10−53×10−5=0.80M\Rightarrow [N_2O_5]=\frac{Rate}{k}=\frac{2.40\times10^{-5}}{3\times10^{-5}}=0.80 M