By what factor does the rate change in each of the following cases (assuming constant temperature)? (a) a reaction is first order in reactant a, and [a] is doubled. (b) a reaction is second order in reactant b, and [b] is halved. (c) a reaction is second order in reactant c, and [c] is tripled.

a) 2

b) 1/4

c) 9

Explanation:

a) for a first order reaction in reactant A

r initial = k*[A initial]

then if the concentration is doubled [A final ]= 2*[A initial]  , then

r final = k*[A final ] = 2* k*[A initial] = 2*r initial

then the velocity changes by a factor of 2

b) for a second order reaction in reactant B

r initial = k*[B initial]²

then if the concentration is halved: [B final ]= [B initial]/2  , then

r final = k*[B final ]²  = k*( [B initial]/2 )²  =k* [B initial]² /4 = r initial /4

then the velocity changes by a factor of 1/4

c) for a second order reaction in reactant C

r initial = k*[C initial]²

then if the concentration is tripled : [C final ]= 3* [C initial]  , then

r final = k*[C final ]²  = k*( 3*[C initial] )²  =k* [C initial]² *9 = 9 * r initial  

then the velocity changes by a factor of 9

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