What is the pH of a solution in which 121 mL of HCl(g), measured at and 0.855 atm, is dissolved in 1.5 L of aqueous solution?

Verified step by step guidance

1. Determine the number of moles of HCl gas using the ideal gas law: PV = nRT. Use the given pressure (P), volume (V), and assume standard temperature (T = 273.15 K) to solve for n (moles of HCl).
2. Convert the volume of HCl gas from mL to L for consistency in units.
3. Calculate the concentration of HCl in the solution by dividing the number of moles of HCl by the volume of the solution in liters (1.5 L).
4. Since HCl is a strong acid, it dissociates completely in water. Therefore, the concentration of HCl is equal to the concentration of H+ ions in the solution.
5. Calculate the pH of the solution using the formula: pH = -\log[H^+].

Key Concepts

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, [H+], in the solution, which is crucial for understanding the strength of acids and bases.

Concentration of HCl

Hydrochloric acid (HCl) is a strong acid that dissociates completely in water, contributing to the concentration of hydrogen ions in the solution. To find the pH, one must first determine the molarity of HCl in the final solution, which involves calculating the number of moles of HCl from its volume and pressure, and then dividing by the total volume of the solution.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, and temperature of a gas to the number of moles. In this context, it is used to calculate the number of moles of HCl gas at a given pressure and volume before it is dissolved in water. This calculation is essential for determining the concentration of HCl in the aqueous solution and subsequently its pH.