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?

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Convert the volume of HCl gas from mL to L by dividing by 1000.

Use the ideal gas law, PV = nRT, to calculate the number of moles of HCl gas. Remember to convert temperature to Kelvin by adding 273.15 to the Celsius temperature.

Calculate the molarity of the HCl solution by dividing the number of moles of HCl by the volume of the solution in liters.

Since HCl is a strong acid, it dissociates completely in water. Therefore, the concentration of H+ ions is equal to the molarity of the HCl solution.

Calculate the pH of the solution using the formula pH = -log[H+].

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Key Concepts

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

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, below 7 indicates acidity, and above 7 indicates basicity. The pH is calculated as the negative logarithm of the hydrogen ion concentration in the solution, which is crucial for understanding the strength of acids and bases.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law allows us to calculate the number of moles of HCl gas present in the solution, which is essential for determining the concentration of hydrogen ions when the gas is dissolved in water.

Concentration and Dilution

Concentration refers to the amount of solute present in a given volume of solution, typically expressed in moles per liter (M). When HCl gas is dissolved in water, its concentration can be calculated by dividing the number of moles of HCl by the total volume of the solution. This concentration directly influences the pH of the solution.

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Textbook Question

Determine the pH of each solution. a. 0.048 M HI b. 0.0895 M HClO₄ c. a solution that is 0.045 M in HClO₄ and 0.048 M in HCl d. a solution that is 1.09% HCl by mass (assume a density of 1.01 g/mL for the solution)

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

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Textbook Question

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