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Chapter 15: Problem 64

Compare the \(\mathrm{pH}\) of a \(0.040 \mathrm{M} \mathrm{HCl}\) solution with that of a \(0.040 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution. (Hint: \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is a strong acid; \(K_{\mathrm{a}}\) for \(\left.\mathrm{HSO}_{4}^{-}=1.3 \times 10^{-2} .\right)\)

Short Answer

Expert verified
The \(0.040 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution is more acidic and thus has a lower pH (approximately 1.1) compared to the\(0.040 \mathrm{M} \mathrm{HCl}\) solution whose pH is approximately 1.4.

Step by step solution

01

Understand the Dissociation of Strong Acids

Strong acids dissociate completely in solution. \(\mathrm{HCl}\) is a strong acid and it will donate one proton (\(\mathrm{H^{+}}\)) per molecule. Therefore, \(\mathrm{[H^{+}]}\) in the \(\mathrm{HCl}\) solution is 0.040 M. The \(\mathrm{H_{2}SO_{4}}\) is also a strong acid, but it can donate two protons (\(\mathrm{2H^{+}}\)) per molecule. That means, theoretically, in the absence of a second dissociation constant \(K_{a2}\), the \(\mathrm{[H^{+}]}\) of the \(\mathrm{H_{2}SO_{4}}\) solution would be 0.080 M which is twice as many protons as the \(\mathrm{HCl}\) solution.
02

Calculate the pH for Each Solution

The pH of a solution can be calculated using the formula \(pH = -log[H^{+}]\). For the \(\mathrm{HCl}\) solution, the calculation is \(pH = -log(0.040)\), which yields a pH of approximately 1.4. Likewise, for the \(\mathrm{H_{2}SO_{4}}\) solution, you will calculate the pH as \(pH = -log(0.080)\), which leads to a pH of approximately 1.1.
03

Compare the pH Levels

From the calculations in Step 2, you can see that the \(\mathrm{H_{2}SO_{4}}\) solution has a lower pH than the \(\mathrm{HCl}\) solution. Remember, lower pH values mean the solution is more acidic. This is consistent with the fact that \(\mathrm{H_{2}SO_{4}}\) donates more protons to the solution than \(\mathrm{HCl}\) does.

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Most popular questions from this chapter

The three common chromium oxides are \(\mathrm{CrO}\), \(\mathrm{Cr}_{2} \mathrm{O}_{3},\) and \(\mathrm{CrO}_{3} .\) If \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) is amphoteric, what can you say about the acid-base properties of \(\mathrm{CrO}\) and \(\mathrm{CrO}_{3} ?\)

Prove the statement that when the concentration of a weak acid HA decreases by a factor of \(10,\) its percent ionization increases by a factor of \(\sqrt{10}\). State any assumptions.

To which of the following would the addition of an equal volume of \(0.60 \mathrm{M} \mathrm{NaOH}\) lead to a solution having a lower pH: (a) water, (b) \(0.30 \mathrm{M}\) HCl, (c) \(0.70 M \mathrm{KOH}\) (d) \(0.40 M \mathrm{NaNO}_{3} ?\)

About half of the hydrochloric acid produced annually in the United States (3.0 billion pounds) is used in metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write the overall and net ionic equations for the reaction between iron(III) oxide, which represents the rust layer over iron, and \(\mathrm{HCl}\). Identify the Brønsted acid and base. (b) Hydrochloric acid is also used to remove scale (which is mostly \(\mathrm{CaCO}_{3}\) ) from water pipes (see Chemistry in Action essay "An Undesirable Precipitation Reaction" in Section 4.2 ). Hydrochloric acid reacts with calcium carbonate in two stages; the first stage forms the bicarbonate ion, which then reacts further to form carbon dioxide. Write equations for these two stages and for the overall reaction. (c) Hydrochloric acid is used to recover oil from the ground. It dissolves rocks (often \(\mathrm{CaCO}_{3}\) ) so that the oil can flow more easily. In one process, a 15 percent (by mass) HCl solution is injected into an oil well to dissolve the rocks. If the density of the acid solution is \(1.073 \mathrm{~g} / \mathrm{mL},\) what is the \(\mathrm{pH}\) of the solution?

Hemoglobin (Hb) is a blood protein that is responsible for transporting oxygen. It can exist in the protonated form as \(\mathrm{HbH}^{+}\). The binding of oxygen can be represented by the simplified equation $$ \mathrm{HbH}^{+}+\mathrm{O}_{2} \rightleftharpoons \mathrm{HbO}_{2}+\mathrm{H}^{+} $$ What form of hemoglobin is favored in the lungs where oxygen concentration is highest? (b) In body tissues, where the cells release carbon dioxide produced by metabolism, the blood is more acidic due to the formation of carbonic acid. What form of hemoglobin is favored under this condition? (c) When a person hyperventilates, the concentration of \(\mathrm{CO}_{2}\) in his or her blood decreases. How does this action affect the above equilibrium? Frequently a person who is hyperventilating is advised to breathe into a paper bag. Why does this action help the individual?
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