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Chapter 12: Problem 1

Practise interconverting pH values and proton concentrations. Express all values to four significant figures. (a) What is a pH \(7.4\) expressed as \(\left[\mathrm{H}^{+}\right]\)in \(\mathrm{mol} \mathrm{L}^{-1} ?\) (b) What is a pH \(4.1\) expressed as \(\left[\mathrm{H}^{+}\right]\)in mol \(L^{-1} ?\) (c) What is the \(\mathrm{pH}\) of a solution of \(\left[\mathrm{H}^{+}\right]\)at \(2 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} ?\) (d) What is the pH of a solution of \(\left[\mathrm{H}^{+}\right]\)at \(2 \times 10^{-12.5} \mathrm{~mol} \mathrm{~L}^{-1} ?\)

Short Answer

Expert verified
The solutions to the exercises are: (a) \([\mathrm{H^{+}}] = 3.981 \times 10^{-8} \) mol/L (b) \([\mathrm{H^{+}}] = 7.943 \times 10^{-5} \) mol/L (c) pH = 4.70 (d) pH = 12.70

Step by step solution

01

Converting pH to proton concentration

For questions (a) and (b), apply the formula for pH to find the concentration of \(\mathrm{H^{+}}\). In general, \([\mathrm{H^{+}}] = 10^{-pH}\). So, for pH = 7.4 and pH = 4.1, we have \([\mathrm{H^{+}}] = 10^{-7.4}\) and \([\mathrm{H^{+}}] = 10^{-4.1}\) respectively.
02

Converting proton concentration to pH

For questions (c) and (d), apply the formula for pH to find the pH value. In general, \(pH = -\log_{10}[\mathrm{H^{+}}]\). So, for \([\mathrm{H^{+}}] = 2 \times 10^{-5}\) mol/L and \([\mathrm{H^{+}}] = 2 \times 10^{-12.5}\) mol/L, the pH values will be \(pH = -\log_{10}(2 \times 10^{-5})\) and \(pH = -\log_{10}(2 \times 10^{-12.5})\) respectively.
03

Calculating the values

Use the previous equations to calculate the values for hydrogen ion concentration and pH. For Step 1, use a scientific calculator to find the values of \([\mathrm{H^{+}}]\) from the given pH values, ensure to round your answer to four significant figures. Similarly, for Step 2, calculate the pH value; remember that when calculating the logarithm of a number that is a product (as in our case), we can separate it into the sum of the logarithms of the multiplying numbers. Continue then by calculating the logarithms separately.
04

Interpretation of the results

The obtained results will provide the corresponding concentrations from pH values and vice versa. they should be interpreted considering that a lower pH value indicates a higher concentration of hydrogen ions, and thus a more acidic solution. On the contrary, a higher pH value indicates a lesser concentration of ions, and hence a more basic (or alkaline) solution.

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Most popular questions from this chapter

Practise using the Henderson-Hasselbalch equation. What are the relative proportions of the deprotonated \(\left(A^{-}\right)\)and protonated (HA) forms of each substance at the following \(\mathrm{pH}\) values: (a) ethanoic acid \(\left(\mathrm{p} K_{\mathrm{a}}=4.8\right.\) ) for use in an experiment at pH 3.8; (b) boric acid \(\left(\mathrm{p} K_{\mathrm{a}}=9.2\right)\) for use in an experiment at pH 9.5; (a) HEPES \(\left(p K_{a}=7.5\right)\) for use in an experiment at \(\mathrm{pH}\) 8.1?
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