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I was given this math question in class last week, but I wasn't ever able to figure it out. I am not bad with exponential growth/decay, but this one is tricking me up. Can you help me, I am having a tough time getting through this problem.

The question, from my Pre-Calculus & Trigonometry class is:
The Chemical acidity of a solution is measured in units of pH: pH = -log[H^+], where [H^+] is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its [H^+] than pure water's, which has a pH of 7?

This is a math-class question, so it shouldn't require a ton of science background. Any and all help is appreciated.

Answer
Hi, this is just a log question like:
2 = log x and how would you find x?
Since the base is 10 you would use the log base 10 inverse operation
10^2 = 10^(log x) => x = 100

Now in your problem you are given that rain's pH is 3.2, so you have
3.2 = - log[H^+] or -3.2 = log[H^+] => 10^(-3.2) = [H^+] for the rain water pH
10^(-3.2) = .0006309573...
Pure Water's pH is 7, so -7 = log[H^+] and 10^(-7) = .0000001
To find how many times more hydrogen ion concentrate rain water has than the hydrogen ion concentrate of pure water divide the pure waters into the rains
.0006309573/.0000001 ~= 6309.57 times more ion concentration.

I hope this helped you. Please feel free to ask a follow up question if you still have questions.

Prof W

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