Question

You have \(505 \mathrm{~mL}\) of a \(0.125 \mathrm{M} \mathrm{HCl}\) solution and you want to dilute it to exactly \(0.100 M\). How much water should you add?

Short answer

Therefore, 126 mL of water should be added to dilute the solution to exactly 0.100 M.

Step-by-step solution

Identify given values

The initial volume \(V_1\) of the HCl solution is 505 mL or 0.505 liters (since the volume in the equation should be in liters), the initial molarity \(M_1\) is 0.125 M, the final molarity \(M_2\) is 0.100 M. We need to find the final volume \(V_2\) to determine how much water is added.

Use the dilution formula to find \(V_2\)

Apply the formula \(M_1V_1 = M_2V_2\) to solve for \(V_2\): substituting the known values, \((0.125 M)(0.505 L) = (0.100 M)(V_2)\) which simplifies to \(V_2 = 0.631 L\)

Find the volume of water added

To find the volume of water added, subtract the initial volume from the final volume. The operation \(0.631 L - 0.505 L\) gives a value of 0.126 L, or 126 mL

Key concepts

HCl solution

A Hydrochloric Acid (HCl) solution is a mixture of HCl gas dissolved in water. HCl is a strong acid, which means it completely dissociates in water, releasing hydrogen ions (H⁺) and chloride ions (Cl⁻). This property is essential in chemistry, especially when calculating reactions and performing titrations.

In the context of the given exercise, understanding the concentration of this solution is crucial. The concentration—or molarity—tells us how much HCl is present in a given volume. This is particularly important when diluting solutions, as you'll want to maintain control over how much active substance remains post-dilution.

molarity

Molarity is a measure of concentration in chemistry, represented by the symbol M. It expresses the number of moles of a solute per liter of solution. This is a convenient way to describe how concentrated a solution is and is represented mathematically as:

• Molarity (M) = \( \frac{moles\ of\ solute}{liters\ of\ solution} \)

For our Hydrochloric Acid example:

• An initial molarity \( M_1 \) of 0.125 M signifies 0.125 moles of HCl is found in each liter of solution.
• The problem asks to dilute this to a molarity \( M_2 \) of 0.100 M, meaning post-dilution, there should be 0.100 moles of HCl per liter of solution.

Understanding molarity helps in predicting how solutions will behave in chemical reactions.

dilution formula

The dilution formula allows chemists to calculate the concentration of a solution after dilution. It is crucial when working with solutions that need adjusting to specific concentrations.

The formula used is:

• \( M_1V_1 = M_2V_2 \)

Here:

• \( M_1 \) and \( V_1 \) are the molarity and volume of the starting solution,
• \( M_2 \) and \( V_2 \) are the molarity and volume of the new solution after dilution.

In the problem, applying this formula enabled calculating the volume post-dilution (\( V_2 \)). By equating \( (0.125 M)(0.505 L) \) with \( (0.100 M)(V_2) \), we found the total volume needed to achieve the target molarity. Subtracting the initial volume from this final volume gives the amount of water added (126 mL). This method is simple yet powerful, ensuring precision in solution preparation.