Problem 22 - Chemistry The Science in Context

Question

What is the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in a solution of hydrochloric acid that was prepared by diluting \(7.5 \mathrm{mL}\) of concentrated \((11.6 M)\) HCl to a final volume of \(100.0 \mathrm{L} ?\)

Step-by-Step Solution

Answer

Answer: The concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the final solution is \(0.00087 \mathrm{M}\).

Step 1: Calculate the moles of HCl

To find the moles of HCl in the initial concentrated solution, we use the formula: Moles = Molarity × Volume Where Molarity = \(11.6 \mathrm{M}\) and Volume = \(7.5 \mathrm{mL} = 0.0075 \mathrm{L}\). Moles of HCl = \((11.6 \mathrm{M}) \times (0.0075 \mathrm{L})\) Moles of HCl = \(0.087 \mathrm{mol}\) So, there are \(0.087\) moles of HCl in the concentrated solution.

Step 2: Apply the dilution formula

To find the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the final solution, we use the dilution formula: \(C_1V_1 = C_2V_2\) Where \(C_1\) is the initial concentration, \(V_1\) is the initial volume, \(C_2\) is the final concentration, and \(V_2\) is the final volume. Here we have \(C_1 = 11.6 \mathrm{M}\), \(V_1 = 0.0075 \mathrm{L}\), and \(V_2 = 100.0 \mathrm{L}\). We need to find \(C_2\), so we can rewrite the dilution formula as: \(C_2 = \frac{C_1V_1}{V_2}\) \(C_2 = \frac{(11.6 \mathrm{M})(0.0075 \mathrm{L})}{(100.0 \mathrm{L})}\) \(C_2 = 0.00087 \mathrm{M}\) So, the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the final solution is \(0.00087 \mathrm{M}\).

Key Concepts

Molarity

Molarity is a key concept in chemistry that describes the concentration of a chemical solution. It is expressed as moles of solute per liter of solution, commonly referred to as "M". The formula for molarity is:

• Molarity = Moles of solute / Volume of solution in liters

In the problem, we used this formula to determine the number of moles of hydrochloric acid in the initial solution.
It's important to convert all units appropriately; volumes should always be in liters when calculating molarity. For example, converting 7.5 mL to 0.0075 L was a crucial step.
Understanding molarity helps in finding how diluted or concentrated a solution is, guiding in safe and effective chemical handling.

Hydrochloric Acid

Hydrochloric acid, often abbreviated as HCl, is a common and strong acid used in various laboratory and industrial applications.
It dissociates completely in water, meaning that each molecule of HCl splits into a hydrogen ion (\(H^+\)) and a chloride ion (\(Cl^-\)).

• This complete dissociation is why hydrochloric acid is considered a strong acid.
• In aqueous solutions, the \(H^+\) ions often bind with water to form hydronium ions \(H_3O^+\).

In our calculation, determining the moles of hydrochloric acid was key to finding the concentration of hydronium ions in the diluted solution.
This understanding is vital, especially when predicting the reactivity and behavior of acids in various contexts.

Chemical Solution Concentration

Chemical solution concentration represents how much solute is dissolved in a given quantity of solvent, impacting the properties and reactions of the solution.
Dilution is a process that reduces the concentration of a solute, in this case, hydrochloric acid, by adding more solvent.
We used the dilution formula \(C_1V_1 = C_2V_2\) to compute the new concentration after dilution:

• \(C_1\) and \(V_1\) are the initial concentration and volume.
• \(C_2\) and \(V_2\) are the final concentration and volume after dilution.

Plugging in our known values, we found the final concentration of hydronium ions in the diluted solution.
Mastery of these concepts allows one to accurately prepare solutions of desired concentrations, essential in scientific and practical applications.