A small amount of reactant \"X\" is added to water containing cyclochemical at a

Question

A small amount of reactant "X" is added to water containing cyclochemical at a concentration of 1E-4 mole/L that undergoes a first-order reaction with cyclochemical with a reaction rate constant of k = 0.2 s^-1 (Assume the volume of water is constant.) The reaction proceeds very quickly relative to mass transfer (i.e. assume during the reaction there is a negligible amount of chemical diffusion from the headspace into the liquid) and the chemical reactant "X" is completely used up after only 5 seconds. What is the concentration (mol/L) of cyclochemical in the water right after this reaction step?

Explanation / Answer

Given

Co = 1 * 10-4 mol/L

k = 0.2 s-1

t = 6 s

first order rate law

-dC/dt = kC

-dC / C = k dt

integrating and applying limits

- ln (C/Co) = kt

sub given values

- ln ( C / 1 * 10-4 mol/L ) = 0.2 s-1 * 6 s

- ln ( C /  1 * 10-4 mol/L ) = 1.2

(C /  1 * 10-4 mol/L ) = exp(-1.2)

C = 0.3012 *  1 * 10-4 mol/L = 0.3 * 10-4 mol/L

so this is concentration of cyclochemical in water right after reaction

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