Question

The reactant concentration in a zero-order reaction was 5.00×10−2 M after 195 s and 2.50×10−2 M after 385 s . What is the rate constant for this reaction? Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.

Answer 1

Answer : The rate constant for this reaction is,
`3.65* 10^(-3)Ms^(-1)`

Explanation :

To calculate the rate constant for zero order reaction, the expression used is:

`\ln [A]=-kt+\ln [A_o]`

where,

`[A_o]` = initial concentration

`[A]` = final concentration =
`5.00* 10^(-2)M` at 195 s

`[A]` = final concentration =
`2.50* 10^(-2)M` at 385 s

k = rate constant = ?

Now put all the given values in the above expression, we get:

`\ln (5.00* 10^(-2))=-k* 195+\ln [A_o]` ............(1)

and,

`\ln (2.50* 10^(-2))=-k* 385+\ln [A_o]` ............(2)

Subtracting 1 from 2, we get:

`\ln (2.50* 10^(-2))-\ln (5.00* 10^(-2))=-k* 385+\ln [A_o]+k* 195-\ln [A_o]`

`\ln (2.50* 10^(-2))-\ln (5.00* 10^(-2))=-k* 385+k* 195`

`-0.693=-190k`

`k=3.65* 10^(-3)Ms^(-1)`

Therefore, the rate constant for this reaction is,
`3.65* 10^(-3)Ms^(-1)`