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Chapter 15: Problem 26

A solution is made by dissolving \(18.4 \mathrm{~g}\) of \(\mathrm{HCl}\) in \(662 \mathrm{~mL}\) of water. Calculate the \(\mathrm{pH}\) of the solution. (Assume that the volume remains constant.)

Short Answer

Expert verified
The pH of the solution is 0.12.

Step by step solution

01

Calculate the moles of HCl

Moles of a substance can be calculated by dividing its mass by its molar mass. The molar mass of HCl is approximately \(36.5 \mathrm{~g/mol}\), and we are given that 18.4 g of HCl is dissolved. Thus, the number of moles of HCl = \( \frac{18.4 \mathrm{~g}}{36.5 \mathrm{~g/mol}} = 0.504 \mathrm{~mol}.\)
02

Determine the volume of the solution in liters

Convert the volume of water from milliliters to liters. 1 L = 1000 mL, so the volume in liters = \( \frac{662 \mathrm{~mL}}{1000 \mathrm{~mL/L}} = 0.662 \mathrm{~L}.\)
03

Calculate the molarity of the solution

Molarity is calculated as the number of moles of solute divided by the volume of the solution in liters. So, the molarity of HCl = \( \frac{0.504 \mathrm{~mol}}{0.662 \mathrm{~L}} = 0.761 \mathrm{~M}.\)
04

Calculate the pH of the solution

pH is calculated as \(-\log[H^+]\). In a solution of a strong acid like HCl, the concentration of H+ is equal to the molarity of the solution. Therefore, the pH = \( -\log[0.761] = 0.12.\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters (L). The formula for calculating molarity (M) is \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].

When solving chemistry problems, understanding molarity is fundamental because it relates the amount of the substance dissolved to the total volume of the solution, allowing us to deduce how concentrated or dilute a solution is. In our example, by dividing the moles of hydrochloric acid (HCl) by the volume of the solution, we can calculate the molarity, which is essential for finding the pH level of the solution.
Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a physical property that is used to convert the mass of a substance to the amount of substance in moles. The molar mass of a compound is calculated by summing up the standard atomic weights of the atoms in its chemical formula.

In this exercise, the molar mass of HCl (\(36.5 \text{ g/mol}\)) provides the conversion factor from the given mass of HCl (\(18.4 \text{ g}\)) to moles. Knowing the molar mass is crucial for accurately determining the number of moles, which plays an integral part in calculating molarity, and ultimately, the pH of the solution.
Logarithm in pH
The pH of a solution is a logarithmic measure of the hydrogen ion concentration (\[H^+\]). The mathematical expression for pH is \[ \text{pH} = -\log[\text{H}^+] \], where the logarithm used is the base-10 logarithm. Logarithms help in converting multiplicative relationships into additive ones, making it easier to handle a wide range of ion concentrations.

pH is crucial in determining whether a solution is acidic or basic. A lower pH value indicates a higher concentration of hydrogen ions, meaning the solution is more acidic. For instance, figuring out the negative log of the molarity of HCl allows us to turn the concentration value into a pH value that easily categorizes the acidity of the solution, as demonstrated in our problem.

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Most popular questions from this chapter

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.

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 Br酶nsted 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?

True or false? If false, explain why each statement is wrong. (a) All Lewis acids are Br酶nsted acids. (b) The conjugate base of an acid always carries a negative charge. (c) The percent ionization of a base increases with its concentration in solution. (d) A solution of barium fluoride is acidic.

The ion product of \(\mathrm{D}_{2} \mathrm{O}\) is \(1.35 \times 10^{-15}\) at \(25^{\circ} \mathrm{C}\). (a) Calculate \(\mathrm{pD}\) where \(\mathrm{pD}=-\log \left[\mathrm{D}^{+}\right]\). (b) For what values of \(\mathrm{pD}\) will a solution be acidic in \(\mathrm{D}_{2} \mathrm{O} ?\) (c) Derive a relation between \(\mathrm{pD}\) and \(\mathrm{pOD}\).

Both the amide ion \(\left(\mathrm{NH}_{2}^{-}\right)\) and the nitride ion \(\left(\mathrm{N}^{3-}\right)\) are stronger bases than the hydroxide ion and hence do not exist in aqueous solutions. (a) Write equations showing the reactions of these ions with water, and identify the Br酶nsted acid and base in each case. (b) Which of the two is the stronger base?
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