Question

A solution is prepared by adding 50.0 mL concentrated hydrochloric acid and \(20.0 \mathrm{mL}\) concentrated nitric acid to 300 mL water. More water is added until the final volume is 1.00 L. Calculate \(\left[\mathrm{H}^{+}\right],\left[\mathrm{OH}^{-}\right],\) and the \(\mathrm{pH}\) for this solution. [Hint: Concentrated HCl is \(38 \%\) HCl (by mass) and has a density of 1.19 g/mL; concentrated HNO_ is 70.\% HNO_3 (by mass) and has a density of \(1.42 \mathrm{g} / \mathrm{mL} .]\)

Short answer

The solution will have an \([\mathrm{H}^{+}]\) concentration of 0.933 M, an \([\mathrm{OH}^{-}]\) concentration of \(1.072 \times 10^{-14}\) M, and a pH of approximately 0.031.

Step-by-step solution

Calculate the mass of HCl and HNO3 added.

To find the mass of HCl and HNO3, we will use the volume of the concentrated acids and their densities: Mass of HCl = Volume of HCl * Density of HCl = 50 mL * 1.19 g/mL = 59.5 g Mass of HNO3 = Volume of HNO3 * Density of HNO3 = 20 mL * 1.42 g/mL = 28.4 g

Find the moles of HCl and HNO3.

We are given the percentage by mass of each acid in the concentrated solution. We’ll use these values to find the moles of each acid: Moles of HCl = (Mass of HCl * % by mass of HCl) / molar mass of HCl = (59.5 g * 0.38) / 36.5 g/mol = 0.620 mol Moles of HNO3 = (Mass of HNO3 * % by mass of HNO3) / molar mass of HNO3 = (28.4 g * 0.70) / 63 g/mol = 0.313 mol

Calculate the concentration of H+ ions.

Since both HCl and HNO3 completely dissociate in water, the H+ ions provided by these acids are simply the sum of moles of these two acids. Total moles of H+ = Moles of HCl + Moles of HNO3 = 0.620 mol + 0.313 mol = 0.933 mol To find the concentration, divide the total moles of H+ by the total volume of the solution (1 L): [H+] = (0.933 mol) / (1 L) = 0.933 M

Find the concentration of OH- ions and calculate pH.

To find [OH-], we need to use the ion product of water, Kw (at 25 °C): Kw = [H+] * [OH-] = 1 × 10^(-14) Now, calculate [OH-]: [OH-] = Kw / [H+] = 1 × 10^(-14) / 0.933 M = 1.072 × 10^(-14) M Finally, the pH can be found using the formula: pH = -log[H+] = -log(0.933) ≈ 0.031

Present the results.

The solution will have a [H+] concentration of 0.933 M, a [OH-] concentration of 1.072 × 10^(-14) M, and a pH of approximately 0.031.

Key concepts

Understanding Acid Dissociation

Acid dissociation refers to the process by which an acid releases hydrogen ions (H⁺) into a solution. In this exercise, both hydrochloric acid (HCl) and nitric acid (HNO₃) are strong acids, meaning they completely dissociate in water. This characteristic makes the calculation of H⁺ concentration straightforward, as the number of moles of the acid directly translates to the number of moles of H⁺ ions produced. Understanding this process is crucial for calculating the acidity of the resulting solution.

Steps in Concentration Calculation

The concentration of ions in a solution is a measure of how much solute is present per unit volume of solution. To find this, we first determine the number of moles of solute. Using the given percentages by mass and densities, we can calculate the mass of each acid. Then, by using their molar masses, we convert these masses into moles. Finally, knowing the final volume of the solution (1 L), we can find the molar concentration by dividing the total moles of solute by this volume.

The Ion Product of Water

The ion product of water ( Kw ) is a constant that relates the concentrations of hydrogen ions ( [H⁺] ) and hydroxide ions ( [OH^-] ) in water at a specific temperature. At 25°C, Kw is equal to 1 × 10^{-14} . Regardless of the solution, the product of the concentrations of these ions must equal Kw. This relationship helps us find unknown ion concentrations if we know the concentration of one of the ions. In this exercise, knowing the [H⁺] allows us to calculate [OH^-] .

Understanding Molarity

Molarity is simply a way to express the concentration of a solution. It is denoted as mol/L or M, representing the number of moles of solute per liter of solution. In our exercise, we calculated the molarity of H⁺ ions to be 0.933 M after dissolving the acids in water. Molarity is a key concept when preparing and analyzing solutions, as it allows chemists to know the exact amount of solute present in a specific volume.

Steps in Solution Preparation

Preparing a solution involves mixing solutes with a solvent to achieve a desired concentration. Here's a simplified procedure:

• Measure and mix the volumes of concentrated acids using their densities to find their masses.
• Calculate moles of HCl and HNO₃ using percentage by mass and molar mass.
• Add these acids to a known volume of water and ensure the final volume is adjusted to 1 L.

This systematic approach ensures that the chemical concentrations are precise, allowing for accurate pH and ion concentration calculations.