The following rate data were obtained at 303 K for the following reaction:
`2A + B to C + D`

What is the rate law? What is the order with respect to each rectant and the overall order? What are the units of the rate constant?

Explanation

The rate law may be expressed as, Rate =`k[A]^(p)[B]^(p)`
Comparing experiments (I) and (III),
`("Rate")_(2) = (k[0.4]^(p)[0.3]^(q))/(k[0.2]^(p)[0.3]^(q)) = (2.88 xx 10^(-1))/(7.2 xx 10^(-2))=4` …………..(i)
`("Rate")_(3) = k[0.4]^(p)[0.3]^(q)=2.88 xx 10^(-1)`...............(ii)
`(("Rate")_(3))/(("Rate")_(2)) = (k[0.4]^(p)[0.3]^(q))/(k[0.2]^(p)[0.3]^(q)) = (2.88 xx 10^(-1))/(7.2 xx 10^(-2)) = (28.8 xx 10^(-2))/(7.2 xx 10^(-2))=4`
`[2]^(p) = [2]^(2)` or p=2.
Compairing experiments (i) and (iv)
`("Rate")_(1)/("Rate_(2)) = k[0.1]^(p)[0.1]^(q)=6.0 xx 10^(-3)`...............(iii)
`("Rate")_(4) = k[0.1]^(p)[0.1]^(q)=2.4 xx 10^(-2)`...........(iv)
`("Rate")_(4)/("Rate")_(1)=(k[0.1]^(p)[0.4]^(q))/(k[0.1]^(p)[0.1]^(q))=(2.4 xx 10^(-2))/(6.0 xx 10^(-3)) = (24 xx 10^(-3))/(6 xx 10^9-3) =4`
`[4]^(q)=[4]^(1)` or q=1
Order w.r. to A=2, Order w.r. to A = 2, Order w.r.t. to B=1
Rate law for the reaction = `k[A]^(2)[B]`
Order with respect to overall reaction =2+1=3
Units of rate constant(k) = `mol^(-2)L^(2)min^(-1)`