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

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.