The rate of reaction: `2NO(g) + Cl_(2) (g) rarr 2NOCl (g)`, becomes doubled when the concentration of `Cl_(2)` is doubled. However, when the concentration of both the reactants are doubled, the rate becomes eight times. What is the order w.r.t. `NO` and w.r.t. chlorine ? What is the total order?

Explanation

`2NO(g) + Cl_(2) (g) rarr 2NOCl (g)`
Let the rate of reaction is
`r_(1) = k[NO]^(alpha).[Cl_(2)]^(beta)` …(i)
`r_(2) = 2r_(1) = k[NO]^(alpha).[2Cl_(2)]^(beta)` ...(ii)
`r_(3) = 8r_(1) = k[2NO]^(alpha).[2Cl_(2)]^(beta)`
`(r_(2))/(r_(1))=(2r_(i))/(r_(1))=(k[NO]^(overset(')a).[2Cl_(2)]^(hat(a)))/(k[NO]^(overset(')a).[Cl_(2)]^(hat(a)))` ...(iii)
`:. (2)^(1) = (2)^(beta)`
`beta = 1`
ismilarly, divide Eq. (iii) by Eq. (i)
`(r_(3))/(r_(1)) = (8r_(1))/(r_(1)) =(k[2NO]^(overset(')a).[2Cl_(2)]^(hat(a)))/(k[NO]^(overset(')a).[Cl_(2)]^(hat(a)))`
`8 = (2)^(alpha).(2)^(beta)`
`8 = (2)^(alpha).(2)^(1)`
`4 = (2)^(alpha)`
`(2)^(2) = (2)^(alpha)`
`alpha = 2`
`:. r = k [NO]^(2)[Cl_(2)]^(1)`
Order w.r.t. `NO = 2`
`:.` Order w.r.t. `Cl_(2) = 1`
Overall order of reaction `= 2 + 1 = 3`