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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.

Respuesta :

Answer : The rate constant for this reaction is, [tex]3.65\times 10^{-3}Ms^{-1}[/tex]

Explanation :

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

[tex]\ln [A]=-kt+\ln [A_o][/tex]

where,

[tex][A_o][/tex] = initial concentration

[tex][A][/tex] = final concentration = [tex]5.00\times 10^{-2}M[/tex] at 195 s

[tex][A][/tex] = final concentration = [tex]2.50\times 10^{-2}M[/tex] at 385 s

k = rate constant = ?

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

[tex]\ln (5.00\times 10^{-2})=-k\times 195+\ln [A_o][/tex]       ............(1)

and,

[tex]\ln (2.50\times 10^{-2})=-k\times 385+\ln [A_o][/tex]        ............(2)

Subtracting 1 from 2, we get:

[tex]\ln (2.50\times 10^{-2})-\ln (5.00\times 10^{-2})=-k\times 385+\ln [A_o]+k\times 195-\ln [A_o][/tex]

[tex]\ln (2.50\times 10^{-2})-\ln (5.00\times 10^{-2})=-k\times 385+k\times 195[/tex]

[tex]-0.693=-190k[/tex]

[tex]k=3.65\times 10^{-3}Ms^{-1}[/tex]

Therefore, the rate constant for this reaction is, [tex]3.65\times 10^{-3}Ms^{-1}[/tex]