Problem 26 - Chemistry Matter and Change

Question

Challenge If 0.5 \(\mathrm{L}\) of 5 \(\mathrm{M}\) stock solution of HCl is diluted to make 2 \(\mathrm{L}\) of solution, how much \(\mathrm{HCl},\) in grams, was in the solution?

Step-by-Step Solution

Answer

The solution contains 91.15 grams of HCl.

Step 1: Determine the amount of moles in the stock solution

First, calculate the number of moles of HCl in the stock solution using the formula for molarity: \[ \text{Moles of HCl} = Molarity \times Volume \]The molarity of the stock solution is 5 M and the volume is 0.5 L. Thus, the moles are:\[ \text{Moles of HCl} = 5 \text{ M} \times 0.5 \text{ L} = 2.5 \text{ moles} \]

Step 2: Calculate the mass of HCl

Next, find the mass of HCl using the molar mass. The molar mass of HCl is approximately 36.46 g/mol. Use the formula:\[ \text{Mass of HCl} = \text{Moles of HCl} \times \text{Molar Mass} \]Substitute the values:\[ \text{Mass of HCl} = 2.5 \text{ moles} \times 36.46 \text{ g/mol} = 91.15 \text{ grams} \]

Step 3: Understand the dilution process

Although the solution is diluted to 2 L, the total moles of HCl do not change as dilution does not affect the amount of solute; it only increases the volume. Therefore, the mass of HCl calculated remains the same even after dilution.

Key Concepts

Understanding Molarity

Molarity is an essential concept in chemistry that refers to the concentration of a solution. It's defined as the number of moles of solute (in this context, HCl) that are present in a unit volume of the solution, commonly expressed in liters. To calculate molarity, you use the formula \( \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \).

In the problem, we have a stock solution with a molarity of 5 M, meaning there are 5 moles of HCl in every liter of that solution. Knowing the molarity helps us determine how much of the chemical is present before any further calculations or processes, such as finding the total number of moles or determining mass, can be performed.

Mass Calculation Techniques

Once you know the number of moles in a solution, calculating the mass can be straightforward. The mass of a chemical compound is determined using its molar mass, which is the mass of one mole of that element or compound. For HCl, the molar mass is approximately 36.46 g/mol.

To find the total mass of HCl in the solution, you simply multiply the number of moles by the molar mass. The equation is: \( \text{Mass (g)} = \text{Moles} \times \text{Molar mass (g/mol)} \).

Using this method in our exercise, we've calculated that 2.5 moles of HCl results in a total mass of 91.15 grams. This straightforward multiplication helps to translate the moles into a tangible measurement of grams, useful for various laboratory and industrial applications.

Essentials of the Dilution Process

The dilution process is a method used to decrease the concentration of a solution by increasing its volume, generally with a solvent like water. During this process, the amount of solute (in this case, HCl) remains constant, meaning the total number of moles doesn’t change even when the solution's volume increases.

The exercise demonstrates that though 0.5 L of the stock solution was diluted to 2 L, the mole count of HCl stayed at 2.5 moles. What changes is the molarity, as it is inversely proportional to the volume. Dilution doesn't affect the mass of the solute, which remains 91.15 grams as previously calculated. This principle is critical for preparing solutions with desired concentrations without altering the quantity of the substance present.