lets organise the data given in the question
[ClO₂] (m) [OH⁻] (m) initial rate (m/s)
0.060 0.030 0.0248
0.020 0.030 0.00276
0.020 0.090 0.00828
rate equation as follows
rate = k [ClO₂]ᵃ [OH⁻]ᵇ
where k - rate constant
we need to find order with respect to ClO₂ therefore lets take the 2 equations where OH⁻ is constant.
1) 0.00276 = k [0.020]ᵃ[0.030]ᵇ
2) 0.0248 = k [0.060]ᵃ[0.030]ᵇ
divide first equation from the second
0.0248/0.00276 = [0.060/0.020]ᵇ
8.99 = 3ᵇ
8.99 rounded off to 9
9 = 3ᵇ
b = 2
order with respect to ClO₂ is 2