`100 cm^3` of 1 M `CH_3COOH` was mixed with `100 cm^3` of 2 M `CH_3OH` to form an ester. The change in the initial rate if eachsolution is diliuted with equal volume of water would be

Options

A. 4 times
B. `0.25` times
C. 2 times
D. `0.5` times

Answer

B

Explanation

`underset(1M)(CH_(3)COOH)+underset(2M)(CH_(3)OH)toCH_(3)COOCH_(3)+H_(2)O`
`r_(1)=k[CH_(3)COOH][CH_(3)OH]=k(1)(1)=2k`
When solution is diluted with equal volume of water, concentration is reduced to half.
`therefore" "r_(2)=k((1)/(2))((2)/(2))=(k)/(2)`
`(r_(1))/(r_(2))=(2k)/(k//2)=4 rArr r_(2) =(r_(1))/(4)=0.25r_(1)`