Dear Shahnaz,

you are right,

first order rate constant K is related in an exponential manner to the concentrations Co and Ct and time t:

Ct = Co*exp(-K*t). When solving for K you will get your formula.

Please have a look at a discussion on first order reaction formula in the answers of some questions some time ago here on RG.:

https://www.researchgate.net/post/How_to_calculate_rate_constant_for_first_order_reaction

https://www.researchgate.net/post/How_can_we_calculate_the_reaction_constant_k_in_the_pseudo-first-order_reaction

thankx Gerhard sir