Determining the time needed for a concentration to fall

[Catherine Bubser 2C]

What values do we plug into the integrated rate laws for initial concentration and final concentration if we aren't given a concertation to start with? For example, if we were asked to calculate the time it took for something to fall to 10% of its initial concentration, how would we use this in the equation?

[Peter DePaul 1E]

For the integrated Rate Laws, I can't really answer your question because it's kind of broad.

For the concentrations I would look to how we derived the formula for half life to calculate this time. I attached an image below (for first order reactions), and my idea is instead of saying use , and instead of having use . I believe that should work out mathematically.

[Catherine Bubser 2C]

Thank you so much!!

[Thomas Gimeno]

if you want to test something like dropping 10% you can just use a hypothetical like plugging in your initial concentration as 1M and your final concentration as .9M. I'm not 100% sure cause I know the rate of change can be dependent on the morality for first order reactions so you mihgt have to know the initial concentration.