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Chapter 13: Problem 32

Consider a \(0.10-M \mathrm{H}_{2} \mathrm{CO}_{3}\) solution and a \(0.10-M \mathrm{H}_{2} \mathrm{SO}_{4}\) solution. Without doing any detailed calculations, choose one of the following statements that best describes the \(\left[\mathrm{H}^{+}\right]\) of each solution and explain your answer. a. The \(\left[\mathrm{H}^{+}\right]\) is less than \(0.10 \mathrm{M}\). b. The \(\left[\mathrm{H}^{+}\right]\) is \(0.10 \mathrm{M}\) c. The \(\left[\mathrm{H}^{+}\right]\) is between \(0.10 \mathrm{M}\) and \(0.20 \mathrm{M}\) d. The \(\left[\mathrm{H}^{+}\right]\) is \(0.20 \mathrm{M}\)

Short Answer

Expert verified
The correct statement is c) The \([\mathrm{H}^{+}]\) of each solution is between \(0.10 \mathrm{M}\) and \(0.20 \mathrm{M}\). This is because for the \(0.10 \mathrm{M} \mathrm{H}_{2}\mathrm{CO}_{3}\) solution (a weak acid), the concentration of H⁺ ions will be less than \(0.10 \mathrm{M}\), while for the \(0.10 \mathrm{M}\mathrm{H}_{2}\mathrm{SO}_{4}\) solution (a strong acid), the concentration of H⁺ ions will be equal to \(0.10 \mathrm{M}\) after the first dissociation with an additional insignificant contribution from the second dissociation step.

Step by step solution

01

Understanding Acid Dissociation

H2CO3 is a weak diprotic acid, which means it can dissociate into ions in two steps: 1) H2CO3 → HCO3⁻ + H⁺ 2) HCO3⁻ → CO3²⁻ + H⁺ However, since H2CO3 is a weak acid, the second dissociation is insignificant, and we can focus on the first dissociation reaction. H2SO4 is a strong diprotic acid, which means it dissociates in two steps: 1) H2SO4 → HSO4⁻ + H⁺ 2) HSO4⁻ → SO4²⁻ + H⁺ However, only the first dissociation step occurs completely (since it is a strong acid), while the second step is relatively weak.
02

Comparing H+ Concentrations

For the 0.10 M H2CO3 solution, the concentration of H+ ions would be between 0 and 0.10 M due to the first dissociation step. Since this is a weak acid, the concentration of H+ ions will be significantly less than 0.10 M. For the 0.10 M H2SO4 solution, the concentration of H+ ions will be equal to 0.10 M after the first dissociation step, as all H2SO4 molecules will dissociate. There will be a small additional contribution of H+ ions from the second dissociation step, but this contribution is very insignificant.
03

Choosing the Correct Statement

Based on the comparisons of H+ concentrations, we can conclude that: a) The [H+] of the H2CO3 solution is less than 0.10 M. This is because it is a weak acid and only the first dissociation occurs partially. b) The [H+] of the H2SO4 solution is close to but slightly greater than 0.10 M. This is because this is a strong acid and the first dissociation occurs completely, while the second dissociation step has an insignificant contribution. Therefore, the answer is: c) The [H+] of each solution is between 0.10 M and 0.20 M.

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