chemistry kinetics rate law

Question

Give the characteristics of a first order reaction having only one reactant

a) the rate of the reattion is not proportional to the concentration of the reactant

b) the rate of the reaction is proportional to the square of the concentration of the reactant

c) the rate of the reaction is proportional to the natural log of the concetration of the reactant

d) the rate of the reaction is directly proportional to the concentration of the reactant

this is a question on my study guide that i thought the answer was c but the answer key says d is correct. I thought that in a first order reaction the rate is = ln[x] at least i think thats what you graph. can anybody explain why d is correct? thanks!

Answer 1

d) the rate of the reaction is directly proportional to the concentration of the reactant is correct because that's what FIRST order means. It means that the rate is directly proportional to the concentration of the reactant. The ln [X] that you refer to has to do with the integrated rate law for a first order reaction, namely...

ln[A] = −kt + ln[A]₀

First order for A ===> B

rate = k[A]