I know how to find half-lives, but I have trouble finding the length of time it would take for the concrentration of X to decrease to Y% of its initial value.

Question

For example, this is one of the problems:

Methyl isocyanide, CH3NC, isomerizes when heated to give acetonitrile (methyl cyanide), CH3CN.

CH3NC(g) ---> CH3CN(g)

The reaction is first order. At 230 degrees, the rate constant for the isomerization is 6.3 x 10-4/s. What is the half-life? How long would it take for the concentration of CH3NC to decrease to 75.0% of its initial value? to 30.0% of its initial value?

I’m not sure if this one would work the same way, but I needed help with this problem as well. If they are done the same way, could you do at least a couple from this 2nd problem when it starts asking for the 25% and 12.5%?

In the presence of excess thiocyanate ion, SCN-, the following reaction is first order in chromium (III) ion, Cr3+; the rate constant is 2.0 x 10-6/s.

What is the half-life in hours? How many hours would be required for the initial concentration of Cr3+ to decrease to each of the following values: 25.0% left, 12.5% left, 6.25% left, 3.125% left?

Any help would be greatly appreciated!!! Thanks!

P.S. Sorry, I couldn't do superscripts on here!

Have you tried t_1/2=0.693/k to obtain half-life?

Have you tried, for the second part of the first problem, assuming you start with 100 molecules (No) of CH3N?. For it to decrease to 75% of its original value means N=75 and plug those values into ln(No/N)=kt and solve for t? Check my thinking.