For the reaction `2x + y rarr L`. Find the rate law from the following data.
`{:([X],[Y],"rate"),("(min)","(min)",(M s^(-1))),(0.2,0.02,0.15),(0.4,0.02,0.30),(0.4,0.08,1.20):}`

Explanation

Rate `k[x]^(n)[y]^(m)`
`0.15=k[0.2]^(n)[0.02]^(m)" "` …(1)
`0.30=k[0.4]^(n)[0.2]^(m) " "` ….(2)
`1.20=k[0.4]^(n)[0.08]^(m) " "` ….(3)
By dividing equation `((3))/((2))`
`(1.2)/(0.3)=(k[0.4]^(n)[0.08]^(m))/(k[0.4]^(n)[0.02]^(m))`
`4=(([0.08])/([0.02]))^(m)`
` 4 = (4)^(m)`
`therefore m = 1`
By diving equation `((2))/((1))`
`rArr (0.30)/(0.15)=(k[0.4]^(n)[0.02]^(m))/(k[0.2]^(n)[0.02]^(m))`
`rArr 2=(([0.4])/([0.2]))^(n)`
`2=(2)^(n)`
`therefore n = 1`
Rate `= k [x]^(1)[y]^(1)`
`0.15 = k[0.2]^(1)[0.02]^(1)`
`(0.15)/([0.2]^(1)[0.02]^(1))=k`
`k = 37.5 mol^(-1)L s^(-1)`