What volume of a concentrated HCl solution, which is 36.0% HCl by mass and has a density of 1.179 g/mL, should be used to make 5.00 L of an HCl solution with a pH of 1.8?

Verified step by step guidance

Determine the concentration of the target HCl solution using the pH value. Use the formula \( \text{pH} = -\log[\text{H}^+] \) to find \([\text{H}^+]\).

Calculate the molarity of the target HCl solution. Since \([\text{H}^+]\) is equal to the molarity of HCl, use the value from the previous step.

Calculate the molarity of the concentrated HCl solution. Use the given mass percentage and density to find the molarity: \( \text{Molarity} = \frac{\text{mass percent} \times \text{density} \times 1000}{\text{molar mass of HCl}} \).

Use the dilution equation \( M_1V_1 = M_2V_2 \) to find the volume \( V_1 \) of the concentrated solution needed. Here, \( M_1 \) is the molarity of the concentrated solution, \( V_1 \) is the volume of the concentrated solution, \( M_2 \) is the molarity of the target solution, and \( V_2 \) is the volume of the target solution.

Solve for \( V_1 \) to find the volume of the concentrated HCl solution required.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concentration and Dilution

Concentration refers to the amount of solute present in a given volume of solution. In this context, diluting a concentrated HCl solution involves mixing it with a solvent (usually water) to achieve a desired concentration. The dilution equation, C1V1 = C2V2, where C is concentration and V is volume, is essential for calculating the volume of concentrated solution needed to achieve a specific concentration in a larger volume.

pH and Hydrogen Ion Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration (H+). A pH of 1.8 indicates a relatively high concentration of H+ ions, which can be calculated using the formula [H+] = 10^(-pH). Understanding how to relate pH to H+ concentration is crucial for determining the amount of HCl needed to achieve the desired acidity in the final solution.

Density and Mass-Volume Relationships

Density is defined as mass per unit volume and is a critical factor in converting between mass and volume of a solution. For the concentrated HCl solution, knowing its density (1.179 g/mL) allows us to calculate the mass of HCl in a given volume. This relationship is important for determining how much of the concentrated solution is required to provide the necessary amount of HCl to achieve the target pH in the final diluted solution.

Recommended video:

Guided course

01:56

Density Concepts

Related Practice

Textbook Question

What mass of HI must be present in 0.250 L of solution to obtain a solution with each pH value?

a. pH = 1.25 b. pH = 1.75 c. pH = 2.85

Textbook Question

What mass of HClO₄ must be present in 0.500 L of solution to obtain a solution with each pH value? a. pH = 2.50 b. pH = 1.50 c. pH = 0.50

Textbook Question

What is the pH of a solution in which 224 mL of HCl(g), measured at 27.2 °C and 1.02 atm, is dissolved in 1.5 L of aqueous solution?

Textbook Question

Determine the [H₃O⁺] and pH of a 0.100 M solution of benzoic acid.

Textbook Question

Determine the [H₃O⁺] and pH of a 0.200 M solution of formic acid.

Textbook Question

Determine the pH of an HNO₂ solution of each concentration. In which cases can you not make the simplifying assumption that x is small? a. 0.500 M b. 0.100 M c. 0.0100 M