a) Lemon juice has a pH of 2.3. What is the hydrogen ion concentration?
Well, pH = - log[H+]
Or, in words, pH is equal to -1 multiplied by the logarithm (base 10) of the hydrogen ion concentration.
So you have 2.3 = -log[H+].
We want to isolate the H+, so let’s start simplifying the right hand side of the equation. First, we multiply both sides by -1.
Now, the definition of a logarithm says that if the log (base 10) of [H+] is -2.3, then 10 raised to the -2.3 power is [H+]
So on each side of the equation, we raise 10 to the power of that side of the equation.
10^(-2.3) = 10^(log[H+])
and because 10^log cancels out…
10^(-2.3) = [H+]
Now we’ve solved for [H+], the hydrogen ion concentration! It’s equal to 10^(-2.3), or 0.00501 M, or 5.01 * 10^-3 moles/Liter
pH is defined as the logarithm of the reciprocal of the hydrogen ion concentration:
CONCLUSION: the hydrogen ion concentration is 0.005012 moles per liter, or in scientific notation 5.012×10−3 moles per liter.