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

Verified step by step guidance

1. Step 1: Use the ideal gas law to calculate the number of moles of HCl gas. The ideal gas law is given by: $PV=nRT$, where P is pressure (1 atm), V is volume (15.0 L), R is the gas constant (0.0821 L·atm/(mol·K)), and T is temperature in Kelvin (convert 25 °C to Kelvin by adding 273.15).
2. Step 2: Rearrange the ideal gas law to solve for n (number of moles): $n=\frac{PV}{RT}$. Substitute the values for P, V, R, and T into the equation.
3. Step 3: Perform the calculation to determine the number of moles of HCl gas. This will give you the total moles of HCl that dissolve in the water, as the problem states that all the HCl dissolves.
4. Step 4: Note that the volume of water (250.0 mL) does not directly affect the calculation of moles of HCl, as the problem focuses on the gas dissolving into the solution. However, this volume may be relevant for subsequent calculations, such as determining molarity.
5. Step 5: Conclude that the number of moles of HCl calculated in Step 3 represents the total moles of HCl in the solution.

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. While the question focuses on the moles of HCl, understanding molarity is essential for determining how concentrated the resulting solution will be after the gas dissolves in water.

Dissolution Process

The dissolution process refers to how a solute (in this case, HCl gas) interacts with a solvent (water) to form a solution. It is important to recognize that when HCl gas dissolves in water, it ionizes to form H⁺ and Cl⁻ ions, which is crucial for understanding the properties of the resulting solution.