# In the  reaction $2A+B\to {A}_{2}B,$ if the concertation of A is doubled and that of B is halved, then the rate of the reaction will

1. A

increases 2 times

2. B

increases 4 times

3. C

decreases 2 times

4. D

remain the same

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### Solution:

$2A+B\to {A}_{2}B$

${r}_{1}=k{\left[A\right]}^{2}\left[B\right]\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}.....\left(i\right)$

When, $\left[A\right]=\left[2A\right],\left[B\right]=\left[\frac{B}{2}\right]$

${r}_{2}=k{\left[2A\right]}^{2}\left[\frac{B}{2}\right]=k4{\left[A\right]}^{2}\frac{\left[B\right]}{2}$

$=k2{\left[A\right]}^{2}\left[B\right]=2{r}_{1}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\because {r}_{1}=k{\left[A\right]}^{2}\left[B\right]\right)$

$\therefore$ Rate of reaction is increased two times

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