What would be the effect on the rate of reaction due to the four-fold increase in a reactant concentration, if the order of reaction were the following:
(a) Zero order , (b) First order
( c) `1//2` order , (d) Fourth order

Explanation

(a) `r_(1) = k[A]^(n)`
When `n = 0`
`r_(1) = k[A]^(0)`
`r_(2) = k[4A]^(0)`
`r_(1) = r_(2)`, (No change in rate)
(b) `r_(1) = k[A]^(n)`,
When `n = 1, r_(1) = k[A]^(1), r_(2) = k[4A]^(1)`
`(r_(2))/(r_(1)) = (k xx 4[A]^(1))/(k xx [A]^(1))`
`r_(2) = 4r_(1) rArr 4` times
( c) When `n = (1)/(2), r_(1) = k[A]^((1)/(2)), r_(2) = k[4A]^((1)/(2))`
`(r_(2))/(r_(1)) = (4)^(1//2)`
`:. r_(2) = 2r_(1) rArr 2 "times"`
(d) `r_(1) = k[A]^(4), r_(2) = k[4A]^(4)`, when `n = 4`
`(r_(2))/(r_(1)) = (k[4]^(4)[A]^(4))/(k[A]^(4))`
`r_(2) = 256 r_(1) rArr 256 "times"`