A solution is prepared by bubbling 15.0 L of HCl(g) at 25 °C and 1 atm into 250.0 mL of water. Assuming all the HCl dissolves in the water, how many moles of HCl are in solution?

Verified step by step guidance

1. Identify the ideal gas law equation: PV = nRT.
2. Rearrange the equation to solve for n (moles): n = \frac{PV}{RT}.
3. Substitute the given values into the equation: P = 1 atm, V = 15.0 L, R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}, T = 25 \degree C (convert to Kelvin by adding 273.15).
4. Calculate the temperature in Kelvin: T = 25 + 273.15.
5. Substitute all values into the equation to find the number of moles of HCl.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it allows us to calculate the number of moles of HCl gas by using the given volume (15.0 L), pressure (1 atm), and temperature (25 °C).

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this problem, understanding molarity is essential for determining how the moles of HCl gas translate into a concentration when dissolved in 250.0 mL of water.

Dissolution Process

The dissolution process refers to the interaction between solute and solvent that results in the solute becoming evenly distributed within the solvent. In this case, it is important to assume that all HCl gas dissolves in water, which simplifies the calculation of moles in solution without considering any losses or incomplete reactions.