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Chapter 15: Problem 17

Calculate the \(\mathrm{pH}\) of each of the following solutions: (a) \(0.0010 \mathrm{MHCl}\), (b) \(0.76 M\) KOH.

Short Answer

Expert verified
The pH of the \(0.0010 \mathrm{MHCl}\) solution is 3.0 and the pH of the \(0.76 M \mathrm{KOH}\) solution is 13.12.

Step by step solution

01

Calculate pH of the HCl solution

Given the molarity (M) of the HCl solution as 0.0010 M. Because HCl is a strong acid, it fully dissociates in water to give H+ ions, so the concentration of H+ ions will be the same as the molarity of the solution. Therefore, the pH of the solution can be calculated using the formula: \(\mathrm{pH} = - \log[\mathrm{H^+}]\). Substituting the known H+ concentration, the pH of the solution is calculated as \( \mathrm{pH} = - \log(0.0010) = 3.0 \).
02

Calculate pOH of the KOH solution

Given the molarity (M) of the KOH solution as 0.76 M. KOH is a strong base which fully dissociates in water to give OH- ions. So the concentration of OH- ions is the same as the molarity of the KOH solution. The pOH of the solution can be calculated using the formula: \(\mathrm{pOH} = - \log[\mathrm{OH^-}]\). By substituting the known OH- concentration: \(\mathrm{pOH} = - \log(0.76) = - \log(7.6 \times 10^{-1}) = - (-0.88) = 0.88\).
03

Calculate pH of the KOH solution

The pH can be found using the relation \( \mathrm{pH} = 14 - \mathrm{pOH} \). Substituting the known pOH: \(\mathrm{pH} = 14 - 0.88 = 13.12 \).

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Most popular questions from this chapter

Novocaine, used as a local anesthetic by dentists, is a weak base \(\left(K_{\mathrm{b}}=8.91 \times 10^{-6}\right) .\) What is the ratio of the concentration of the base to that of its acid in the blood plasma \((\mathrm{pH}=7.40)\) of a patient?

A solution contains a weak monoprotic acid HA and its sodium salt NaA both at \(0.1 M\) concentration. Show that \(\left[\mathrm{OH}^{-}\right]=K_{\mathrm{w}} / K_{\mathrm{a}}\).

Without referring to the text, write the formulas of four strong acids and four weak acids.

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?

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 \(\mathrm{CrO}_{3} ?\)
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