Problem 82 - Chemistry Matter and Change

Question

If 5.00 mL of 6.00\(M\) HCl is added to 95.00 mL of pure water, the final volume of the solution is 100.00 \(\mathrm{mL}\) . What is the pH of the solution?

Step-by-Step Solution

Answer

To find the pH of the solution, first calculate the moles of HCl in the initial solution: 0.005 L × 6.00 M = 0.030 moles. Then, calculate the final concentration of HCl: 0.030 moles / 0.100 L = 0.300 M. Finally, calculate the pH: -log(0.300) = 0.52. Therefore, the pH of the solution is approximately 0.52.

Step 1: Calculate the number of moles of HCl in the initial solution

We know that the volume of the HCl solution is 5.00 mL and its concentration is 6.00 M. We can use the equation: Moles of solute = Volume of solution × Concentration Convert the volume of HCl from mL to L: 5.00 mL = 0.005 L Moles of HCl = 0.005 L × 6.00 M = 0.030 moles So, there are 0.030 moles of HCl in the initial solution.

Step 2: Calculate the final concentration of HCl in the solution

Now that we have the number of moles of HCl, we can find the final concentration of HCl in the mixture. To do this, we can use the following formula: Final concentration = Moles of solute / Final volume of solution The total final volume of the solution is given as 100.00 mL or 0.100 L. Thus: Final concentration = 0.030 moles / 0.100 L = 0.300 M

Step 3: Calculate the pH

We are now ready to calculate the pH of the solution. The pH is defined as the negative logarithm (base 10) of the concentration of H+ ions in the solution. Hydrochloric acid is a strong acid and is assumed to dissociate completely in water, so the concentration of H+ ions is equal to the concentration of HCl. pH = -log[H+] pH = -log(0.300) = 0.52 So, the pH of the solution is approximately 0.52.

Key Concepts

Understanding Molarity

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution. In simpler terms, molarity (often denoted as \(M\)) tells us how much of a chemical is present in a given volume of liquid.
For example, if a solution has a molarity of 6.00M, this means there are 6.00 moles of solute, such as hydrochloric acid (HCl), in every liter of solution. In the exercise, a 5.00 mL sample of a 6.00M HCl solution is used. Converting this to liters (0.005 L), the number of moles is calculated as the product of volume and molarity:

• Moles of HCl = 6.00M × 0.005L = 0.030 moles

This basic calculation is crucial for determining how concentrated a solution is before dilution or further reactions.

Acid Dissociation

Acid dissociation refers to how acids release hydrogen ions (\(H^+\)) when they dissolve in water. This is a key concept for calculating the pH of a solution because the amount of \(H^+\) directly affects the pH value.
Strong acids like HCl dissociate completely in water. This means every molecule of HCl in water will donate an \(H^+\) ion to the solution. Therefore, the concentration of \(H^+\) ions is equal to the initial concentration of the acid.
Understanding dissociation is vital to pH calculations:

• Strong acids dissociate completely: [HCl] = [H⁺]
• Weaker acids partially dissociate: Not all molecules release \(H^+\) ions

For the exercise, since HCl is strong, the [HCl] of 0.300M leads to an \([H^+]\) of 0.300M in the solution.

Hydrogen Ion Concentration and pH

The hydrogen ion concentration in a solution is directly related to its pH. The pH is a measure of the acidity or basicity of a solution, determined using the formula \(pH = -\log[H^+]\).
A low pH value indicates a high concentration of hydrogen ions and thus a very acidic solution. Conversely, a high pH value suggests a low concentration of hydrogen ions and a basic solution.
Our calculation focuses on the concentration of \([H^+]\), which directly comes from our dissociated HCl acid. Given a concentration of 0.300M, the pH is calculated as:

• \(pH = -\log(0.300) = 0.52\)

This tells us the solution is highly acidic, as expected from a solution of hydrochloric acid.

Solution Dilution

Solution dilution involves adding a solvent, such as water, to a solution, which reduces the concentration of the solute. This is explored in the exercise as we initially had a 6.00M HCl solution that was diluted by adding water to increase the total volume to 100.00 mL.
The dilution formula, \(C_1V_1 = C_2V_2\), can help us understand the concept:

• \(C_1\) is the initial concentration (6.00M)
• \(V_1\) is the initial volume (5.00 mL)
• \(C_2\) is the final concentration (calculated as 0.300M)
• \(V_2\) is the final volume (100.00 mL)

By using this relationship, the final molarity after dilution was calculated to be 0.300M. Dilution has the effect of lowering the concentration of \(H^+\) ions, thereby having an impact on the pH of the solution.