How many milliliters of concentrated hydrochloric acid solution (36.0% HCl by mass, density = 1.18 g/mL) are required to produce 10.0 L of a solution that has a pH of 2.05?

Verified step by step guidance

Calculate the concentration of hydrogen ions \([H^+]\) in the target solution using the pH value. Use the formula \([H^+] = 10^{-\text{pH}}\).

Determine the molarity of the target solution. Since \([H^+]\) is equal to the molarity of HCl in the solution, use the concentration from step 1.

Calculate the moles of HCl needed in the target solution by multiplying the molarity from step 2 by the volume of the solution in liters (10.0 L).

Determine the mass of HCl required using the moles calculated in step 3 and the molar mass of HCl (36.46 g/mol).

Calculate the volume of the concentrated HCl solution needed. Use the mass of HCl from step 4, the percentage by mass (36.0%), and the density (1.18 g/mL) to find the volume in milliliters.

Key Concepts

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

pH and Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. A pH of 2.05 indicates a relatively high concentration of hydrogen ions, which can be calculated using the formula [H+] = 10^(-pH). This relationship is crucial for determining how much hydrochloric acid is needed to achieve the desired pH in the final solution.

Mass Percent Concentration

Mass percent concentration expresses the mass of solute in a given mass of solution, calculated as (mass of solute / mass of solution) x 100%. In this case, the concentrated hydrochloric acid solution is 36.0% HCl by mass, meaning that in 100 g of solution, there are 36 g of HCl. This concept is essential for converting between mass and volume when calculating the amount of acid needed.

Density and Volume Calculations

Density is defined as mass per unit volume (g/mL), and it allows for the conversion between mass and volume of a substance. For the concentrated hydrochloric acid solution with a density of 1.18 g/mL, this means that 1 mL of solution weighs 1.18 g. Understanding how to use density in calculations is vital for determining the volume of concentrated acid required to achieve the target concentration in the final solution.

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