For a given reaction, , X ( g )+ Y ( g Z ( g ) , the order of reaction with respect to X and Y are m and n respectively. If the concentration of X is tripled and that of Y is decreased to one third, what is the ratio between the new rate to the original rate of the reaction?

Step-by-step solution

The rate law for the reaction X ( g ) + Y ( g ) Z ( g ) is given by r₁ = k[X]^m [Y]^n . When the concentration of X is tripled, [X]' = 3[X] . When the concentration of Y is decreased to one third, [Y]' = 1 3 [Y] . The new rate of reaction r₂ is given by r₂ = k(3[X])^m ( 1 3 [Y] )^n . r₂ = k 3^m [X]^m 3^ -n [Y]^n . r₂ = 3^ m-n k[X]^m [Y]^n . r₂ = 3^ m-n r₁ . Therefore, the ratio of the new rate to the original rate is r₂ r₁ = 3^ m-n . Answer: 3^ (m-n)