The rate of reaction, `2NO + Cl_2 to 2NOCI` is doubled when concentration of `Cl_2` is doubled and it becomes 8 times when concentrations of both NO and `Cl_2` are doubled. Deduce the order of this reaction.

Answer

3

Explanation

The rate of reaction is given as: Rate `= k [NO]^x [Cl_2]^y `
According to the given data:

For experiment `1, 1 =k(0.1)^x (0.1)^y`
For experiment 2`,2 =k(0.1)^x (0.2)^y`
For experiment `3,8=k(0.2)^x (0.2)^y`
Dividing eq. (i) by (ii), we get
` 1/2 = ( k ( 0.1)^x ( 0.1)^y )/( k(0.1 ) ^x ( 0.2 ) ^y ) or (1/2)^1 = (1/2)^y` hence y=1
Dividing eq. (ii) by (iii), we get
` 2/8 = (k (0.1 )^x ( 0.2 )^y )/(k( 0.2 )^x (0.2 )^y) or (1/2)^2 = (1/2)^x ` hence ,x=2
` therefore ` Rate `= k[NO]^2 [Cl_2]^1`
Hence, order of reaction = 2 + 1 = 3.