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\mathrm{\quad P_2 \underset{a_{-1}}{\stackrel{a_1}{\leftrightarrows}} 2 P} for a elementary chemical reaction, the expression for\mathrm{ \frac{d[P]}{d t} } is

Option: 1

\mathrm{2 a_1\left[P_2\right]-2 a_{-1}[P]^2}


Option: 2

\mathrm{2 a_1\left[P_2\right]-a_{-1}[P]^2}


Option: 3

\mathrm{a_1\left[p_2\right]+a_{-1}[p]^2}


Option: 4

\mathrm{a_1\left[P_2\right]-a_{-1}[P]^2}


Answers (1)

best_answer

\mathrm{\text { For a reaction, } p_2 \stackrel{a_1}{\longrightarrow} 2 p}

\mathrm{\begin{aligned} & r_f=-\frac{d\left[P_2\right]}{d t}=\frac{1}{2}\left(\frac{d[P]}{d t}\right)_1=a_1\left[P_2\right] \\ & \left(\frac{d[P]}{d t}\right)_1=2 a_1\left[P_2\right] \end{aligned}}

\mathrm{\text { for the } r_{x n} ; 2 P \stackrel{a-1}{\rightarrow} P_2}

\mathrm{r_b=\frac{-1}{2}\left(\frac{d[P]}{d t}\right)_2=a_{-1}[P]^2}

\mathrm{\left(\frac{d[P]}{d t}\right)_2=-2 a_{-1}[P]^2}

Hence overall \mathrm{r_{xn}} will be 

\mathrm{\frac{d[P]}{d t}=2 a_1\left[P_2\right]-2 a_{-1}[P]^2}

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Gunjita

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