For the ozonolysis of pentene in `C Cl_(4)` at 300 K `C_(5)H_(10)+O_(3) rarr C_(5) H_(10)O_(3)` the following data is given
`{:([C_(5)H_(10)],[O_(3)],"rate",),(1.0xx10^(-2),2.8xx10^(-3),2.2,),(0.5xx10^(-2),2.8xx10^(-3),1.1,),(1.0xx10^(-2),5.6xx10^(-3),4.4,):}`
The over all order of reaction is

Options

A. 2
B. 3
C. 1
D. zero

Answer

A

Explanation

Rate `k=[C_(5)H_(10)]^(x)[O_(3)]^(y)`
Order of reaction `=x+y`
`(r_(1))/(r_(2))=(2.2 "mol L"^(-1)"s"^(-1))/(1.1 "mol L"^(-1)"s"^(-1))`
`=((1.0xx10^(-2)"mol L"^(-1))^(x)(2.8xx10^(-3)"mol L"^(-1))^(y))/((0.5xx10^(-2)"mol L"^(-1))^(x)(1.8xx10^(-3)"mol L"^(-1))^(y))`
`2=(2)^(x)`
`:. x=1` with respect to `C_(5)H_(10)`
`(r_(3))/(r_(1))=(4.4 "mol L"^(-1)s^(-1))/(1.1 "mol L"^(-1)s^(-1))`
`=((1.0xx10^(-2)"mol L"^(-1))^(x)(5.6 xx10^(-3)"mol L"^(-1))^(y))/((0.5xx10^(-2)"mol L"^(-1))^(x)(2.8xx10^(-3)"mol L"^(-1))^(y))`
or `4 (2)^(x) (2)^(y)`
But `x = 1 rArr y= 1`
Thus order w.r.t. `O_(3)` is 1
`:.` Overall order of reaction `=x+y =1 + 1=2` .