The decomposition of SOCl2 is first-order in SOCl2. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl2 to drop from 0.36M to 0.045M?

Please help explain half-life and how to do the problem.

Question

The decomposition of SOCl2 is first-order in SOCl2. If the half-life for the reaction is 4.1 hr, how long would it take for the concentration of SOCl2 to drop from 0.36M to 0.045M?

Please help explain half-life and how to do the problem.

aaronq · Answer

for a first order reaction, you can use:  $t_{1/2}=\dfrac{ln2}{k}$, to find k, the decay constant. After you can use the exponential growth/decay equation: 

                              $A_{t}=A_0*e^{-kt}$

where $A_{t}$ is the amount after t time elapsed, $A_0$ is the initial amount. t is time, and k is the decay constant (you found above).

anonymous · Answer

A0 is 0.36

aaronq · Answer

yep

anonymous · Answer

A(t) is 0.045M

aaronq · Answer

correct

anonymous · Answer

So the 4.1 hr would be the t right? But what I'm confuse about is the rate constant (-k) and the e?

aaronq · Answer

e is eulers number, and the k is the constant you found using the first equation by plugging in the half life ($t_{1/2}$). t is what you're solving for

anonymous · Answer

I never did the first equation to this problem.

anonymous · Answer

I think I figured it out. 4.1h is equal to 14760s. Since k equals the rate reaction is 4.97E-5.
By taking the In 0.045/0.36 which equals -4.97E-5 we get 2.08. 2.08 divide into 4.97E-5 which is 41839.9s equals t.

anonymous · Answer

Thanks for the help.