Question

A solution is made by dissolving \(18.4 \mathrm{~g}\) of \(\mathrm{HCl}\) in enough water to make \(662 \mathrm{~mL}\) of solution. Calculate the \(\mathrm{pH}\) of the solution at \(25^{\circ} \mathrm{C}\)

Short answer

The pH of the solution is approximately 0.117.

Step-by-step solution

Calculate Moles of HCl

First, find the moles of HCl by using its molar mass. The molar mass of HCl is 36.46 g/mol. Use the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). So, \( \text{moles of HCl} = \frac{18.4 \text{ g}}{36.46 \text{ g/mol}} \approx 0.505 \text{ moles} \).

Calculate Molarity of the Solution

To find the molarity (M) of the solution, divide the moles of HCl by the volume of the solution in liters. First, convert 662 mL to liters: \( 662 \text{ mL} = 0.662 \text{ L} \). Then use the formula: \( \text{Molarity} = \frac{\text{moles}}{\text{volume in liters}} \). This gives us: \( M = \frac{0.505 \text{ moles}}{0.662 \text{ L}} \approx 0.763 \, \text{M} \).

Relate Concentration to \([H^+]\)

Given that HCl is a strong acid, it dissociates completely in water. The concentration of hydrogen ions \([H^+]\) in solution is equal to the molarity of HCl, which is 0.763 M.

Calculate the pH of the Solution

Use the formula for pH: \( \text{pH} = -\log_{10} ([H^+]) \). Substitute \([H^+] = 0.763\text{ M}\): \( \text{pH} = -\log_{10} (0.763) \approx 0.117 \).

Key concepts

Moles of HCl

To find the moles of a substance, you need to know its mass and its molar mass. Molar mass is the weight of one mole of a substance and is measured in g/mol.
For hydrochloric acid (HCl), the molar mass is 36.46 g/mol. Using the formula for moles, \(\text{moles} = \frac{\text{mass}}{\text{molar mass}},\)we can calculate the moles of HCl from its mass of 18.4 g. By dividing 18.4 g by 36.46 g/mol, we find approximately 0.505 moles.
Understanding the concept of moles helps in quantifying the amount of a substance involved in a chemical reaction, which, in this case, helps us proceed with further calculations related to the solution's properties.

Molarity of Solution

Molarity is a measure of how concentrated a solution is. It tells us how many moles of solute are present in one liter of solution. To find the molarity, you divide the number of moles of solute by the volume of the solution in liters.
Here, we have calculated 0.505 moles of HCl, and the total volume of solution is 662 mL. First, convert the volume from milliliters to liters, which gives you 0.662 L. Then use the formula: \(\text{molarity (M)} = \frac{\text{moles}}{\text{volume in liters}}.\)Hence, the molarity of the solution is about 0.763 M.
This value tells us the concentration of HCl in the solution and is crucial for understanding how strong your solution is in terms of its reactive capacity.

Strong Acids

Strong acids are characterized by their ability to dissociate completely in water. This means they release all of their hydrogen ions (H⁺) into the solution. HCl is a classic example of a strong acid, where in aqueous solution, it dissociates fully into H⁺ ions and Cl⁻ ions.
Because of this complete dissociation, the concentration of H⁺ ions in the solution is equal to the initial concentration of the strong acid. In our example, the molarity of HCl is 0.763 M, and so is the concentration of H⁺.
Understanding the behavior of strong acids is essential because they impact the acidity of a solution significantly, playing a crucial role in calculating the pH accurately.

Hydrogen Ion Concentration

The concentration of hydrogen ions \( [H^+] \) in a solution is a key determinant of its acidity. For strong acids, like HCl, this concentration is equal to the acid's molarity because they completely dissociate in water.
In our example, the molarity of HCl is 0.763 M, so \( [H^+] = 0.763 \, \text{M} \).This relationship simplifies the process of calculating the pH, as you can directly use the molarity as the concentration of H⁺ ions.
The pH scale is used to measure how acidic or basic a solution is, using the formula:\(\text{pH} = -\log_{10} ([H^+]).\)With \( [H^+] = 0.763 \text{ M} \), we calculate the pH to be approximately 0.117. This low pH value confirms the solution's high acidity.