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For a reaction, X+Y rarr Product , quadrupling [x], increases the rate by a factor of 8. Quadrupling both [x] and [y], increases the rate by a factor of 16. Find the order of the reaction with suspect to x and y. what is the overall order of the reaction? |
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Answer» Solution :`""x+y RARR "Product (z)"` `"" x+y rarr z` Condition - 1 `rArr 4x+y rarr 8` Condition - 2 `rArrr 4x+4y rarr 16` `""z=k[x]^(m)[y]^(n)"………………….(1)"` `""8Z=k[4x]^(m)[y]^(n)"......................(2)"` `""16z=k[4x]^(m)[4y]^(n)".....................(3)"` Dividing EQ (2) by Eq (1) we get, `(8z)/z=(k[4x]^(m)[y]^(n))/(k[x]^(m)[y]^(n))` `8=4^(m) rArr 2^(3)=(2^(2))^(m) rArr 2^(3)=2^(2m), 2m=3, m=3//2` 1.5 order with respect to x. Dividing Eq (3) by Eq (1) we get, `""(16z)/z=(k[4x]^(m)[4y]^(n))/(k[x]^(m)[y]^(n))` `""16=4^(m).4^(n)` `""16=4^(2).4^(n)` `""16/16=4^(n)` `""1=4n` `""THEREFORE n=0` [Zero order with respect to y] Overall order of the reaction, `""k[x]^(m)[y]^(n)` `""k[x]^(1.5]y^(0)` Order `=(1.5+0)=1.5` |
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