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Chapter 16: Problem 33

By what factor does \(\left[\mathrm{H}^{+}\right]\) change for a pH change of (a) 3.0 units, (b) 0.3 units?

Short Answer

Expert verified
The concentration of hydrogen ions (\([\mathrm{H}^{+}]\)) changes by a factor of (a) \(10^{-3}\) or \(0.001\) for a pH change of 3.0 units, and (b) \(10^{-0.3}\) or approximately \(0.501\) for a pH change of 0.3 units.

Step by step solution

01

Calculate the initial and final pH values

We are given that the pH change is 3.0 units. Let the initial pH be \(pH_{i}\) and the final pH be \(pH_{f}\). So, we can write \(pH_{f} = pH_{i} + 3\).
02

Use the pH formula to find the change in H+ concentration

We know that \(pH = -\log_{10}([\mathrm{H}^{+}])\). Thus, we have: Initial H+ concentration: \([\mathrm{H}^{+}]_{i}=10^{-pH_{i}}\) Final H+ concentration: \([\mathrm{H}^{+}]_{f}=10^{-pH_{f}}=10^{-(pH_{i}+3)}\)
03

Calculate the factor by which the H+ concentration changes

We have to find the factor \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}}\): \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}} = \frac{10^{-(pH_{i}+3)}}{10^{-pH_{i}}}\) By dividing exponents: \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}} = 10^{-3}\) So the H+ concentration changes by a factor of \(10^{-3}\) or \(0.001\). (b) For a pH change of 0.3 units:
04

Calculate the initial and final pH values

We are given that the pH change is 0.3 units. We can write \(pH_{f} = pH_{i} + 0.3\).
05

Use the pH formula to find the change in H+ concentration

We have: Initial H+ concentration: \([\mathrm{H}^{+}]_{i}=10^{-pH_{i}}\) Final H+ concentration: \([\mathrm{H}^{+}]_{f}=10^{-pH_{f}}=10^{-(pH_{i}+0.3)}\)
06

Calculate the factor by which the H+ concentration changes

We have to find the factor \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}}\): \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}} = \frac{10^{-(pH_{i}+0.3)}}{10^{-pH_{i}}}\) By dividing exponents: \(\frac{[\mathrm{H}^{+}]_{f}}{[\mathrm{H}^{+}]_{i}} = 10^{-0.3}\) So the H+ concentration changes by a factor of \(10^{-0.3}\) or approximately \(0.501\).

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Most popular questions from this chapter

Determine whether each of the following is true or false: (a) All strong bases are salts of the hydroxide ion. (b) The addition of a strong base to water produces a solution of \(\mathrm{pH}>7.0\) (c) Because \(\mathrm{Mg}(\mathrm{OH})_{2}\) is not very soluble, it cannot be a strong base.

Calculate the percent ionization of hydrazoic acid \(\left(\mathrm{HN}_{3}\right)\) in solutions of each of the following concentrations \(\left(K_{a}\right.\) is (c) \(0.0400 \mathrm{M}\). given in Appendix $\mathrm{D}):(\mathbf{a}) 0.400 \mathrm{M},(\mathbf{b}) 0.100 \mathrm{M}$

Write the chemical equation and the \(K_{b}\) expression for the reaction of each of the following bases with water: (a) propylamine, $\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2} ;$ (b) monohydrogen phosphate ion, \(\mathrm{HPO}_{4}^{2-} ;(\mathbf{c})\) benzoate ion, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}$

Is each of the following statements true or false? (a) All strong acids contain one or more H atoms. (b) A strong acid is a strong electrolyte. (c) A 1.0-M solution of a strong acid will have \(\mathrm{pH}=1.0\)

Write the chemical equation and the \(K_{a}\) expression for the acid dissociation of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{HSO}_{4}^{-}\), (b) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}$.
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