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Consider the following reaction, 2NO(g...

Consider the following reaction,
`2NO(g) + CI_(2) (g) to 2NOCI(g)`
The rate of reaction becomes doubled when the concentration of `CI_2` is doubled However, when the concentration of both the reactants are doubled, the rate becomes eight times. What is the order with respect to NO and with respect to reaction chlorine? What is the overall order of reaction?

Text Solution

Verified by Experts

`2NO(g) + CI_(2) (g) to 2NOCI(g)`
Let the rate of reaction be
`r_1 = k [ NO]^(alpha) [CI_2]^( beta)" "...(i)`
`r_2 = 2r_1 = k [NO]^( alpha) [2CI_(2) ]^( beta) " "...(ii)`
`r_3 = 8r_1 = k [2NO]^( alpha) [2CI_2]^( beta)" "...(iii)`
On dividing Eq. (ii) by Eq. (i), we get
`(r_2)/(r_1) = (2r_1)/( r_1) = (k [NO]^( alpha) [2CI_2]^( beta) )/( k[NO]^( alpha) [CI_2]^( beta) )`
`therefore (2)^(1) = (2)^( beta)`
`beta=1`
Similarly, divide Eq. (iii) by Eq. (i), we get
`(r_3)/(r_1) = (8r_1)/(r_1) = (k[2NO]^(alpha) . [2CI_(2) ]^( beta) )/( k[NO]^( alpha) . [CI_(2) ]^( beta) )`
`8 = (2)^( alpha) . (2)^( beta)`
`8 = (2)^( alpha) . (2)^(1) rArr 4 = (2)^( alpha)`
`(2)^(2) = (2)^( alpha) , alpha=2`
`therefore r = k [ NO]^(x) [CI_2 ]^1`
As, order with respect to `NO=2`
Order with respect to `CI_2 = 1`
Overall order of rection `=2+1=3`.
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