Question

A One half liter \((500 . \mathrm{mL})\) of \(2.50 \mathrm{M} \mathrm{HCl}\) is mixed with \(250 .\) mL. of 3.75 M HCl. Assuming the total solution volume after mixing is \(750 .\) mL, what is the concentration of hydrochloric acid in the resulting solution? What is its pH?

Short answer

HCl concentration is 2.92 M; pH is approximately 0.54.

Step-by-step solution

Calculate moles of HCl in first solution

First we need to determine the number of moles of HCl in the first solution. The concentration is given as \(2.50 \, \text{M}\) and the volume is \(500 \, \text{mL} = 0.500 \, \text{L}\). Moles are given by the formula \( \text{moles} = \text{molarity} \times \text{volume} \). So, for the first solution: \[ \text{moles of HCl} = 2.50 \, \text{M} \times 0.500 \, \text{L} = 1.25 \, \text{mol}\]

Calculate moles of HCl in second solution

Now, calculate the number of moles of HCl in the second solution. The concentration is \(3.75 \, \text{M}\) and the volume is \(250 \, \text{mL} = 0.250 \, \text{L}\). Using the same formula: \[ \text{moles of HCl} = 3.75 \, \text{M} \times 0.250 \, \text{L} = 0.9375 \, \text{mol}\]

Calculate total moles of HCl in the mixture

To find the total moles of HCl in the resulting mixture, add the moles from both solutions calculated in Steps 1 and 2. \[ \text{total moles of HCl} = 1.25 \, \text{mol} + 0.9375 \, \text{mol} = 2.1875 \, \text{mol}\]

Calculate concentration of HCl in resulting solution

The concentration of HCl in the resulting solution can be found by dividing the total moles of HCl by the total volume of the solution. The total volume is \(750 \, \text{mL} = 0.750 \, \text{L}\). Thus, the concentration is: \[ \text{concentration} = \frac{2.1875 \, \text{mol}}{0.750 \, \text{L}} = 2.9167 \, \text{M}\]

Calculate the pH of the solution

Since HCl is a strong acid, it fully dissociates in solution. Therefore, the concentration of hydrogen ions \([H^+]\) is equal to the concentration of HCl. To find the pH, use the formula \( \text{pH} = -\log[H^+] \). Thus: \[ \text{pH} = -\log(2.9167) \approx 0.535\]

Key concepts

Solutions mixing

When mixing solutions, particularly for acids like hydrochloric acid (HCl), it's important to understand how their concentrations and volumes affect the final mixture. The process involves combining different solutions to create a new solution with its own unique concentration. This is crucial in many scientific and industrial applications where precise chemical concentrations are required.

In the given problem, two separate solutions with known molarities and volumes are mixed together. A solution with \(2.50 \, \text{M}\) concentration of HCl and \(500 \, \text{mL}\) volume is combined with another solution having \(3.75 \, \text{M}\) concentration of HCl and \(250 \, \text{mL}\) volume. By adding these together, we aim to find the concentration of the new solution.

• First, determine the number of moles for each separate solution using the formula: \( \text{moles} = \text{molarity} \times \text{volume} \).
• Add the moles from both solutions to get the total moles in the mixture.
• Finally, calculate the new concentration by dividing the total moles by the total volume of the combined solution.

This straightforward method helps us anticipate how components combine and what the result will be in terms of their chemical properties.

pH calculation

Calculating the pH of a solution is a fundamental aspect of understanding its acidity or alkalinity. The pH scale ranges from 0 to 14, where a pH less than 7 indicates acidity, greater than 7 indicates basicity, and exactly 7 is neutral. For our scenario, because we are dealing with HCl, a strong acid, the measurement of pH will reveal how acidic the solution is.

The concentration of hydrogen ions \([H^+]\) in solution is crucial because it directly relates to the pH. Since HCl fully dissociates into hydrogen ions and chloride ions in water, the concentration of \([H^+]\) equates to the concentration of the HCl solution itself. We use the formula \( \text{pH} = -\log[H^+] \) to determine the pH.

• For a concentration of \(2.9167 \, \text{M}\), the pH is calculated by taking the negative logarithm of the concentration.
• This calculation gives a pH value of approximately \( ext{0.535}\), indicating a highly acidic solution.
• Such clarity in measurement is critical, especially when preparing solutions for experiments where specific pH levels are required.

Calculating pH accurately informs the handling and usage of the substance, ensuring safety and reliability in its application.

Strong acids

Strong acids are a category of acids that completely dissociate in water, meaning they release all their hydrogen ions into the solution. This characteristic makes strong acids like hydrochloric acid (HCl) very reactive and potent. Understanding the nature of strong acids is essential for handling them safely and using them effectively in various chemical reactions.

When HCl is introduced into water:

• It dissociates completely, providing an equal concentration of hydrogen ions \([H^+]\) and chloride ions \(Cl^-\).
• This complete dissociation is why strong acids have similar concentrations of the acid and \([H^+]\).
• It's also why their calculated pH is so low, representing their high acidity.

For any reaction involving strong acids, we assume full dissociation, which simplifies pH calculations and concentration considerations. Knowing how strong acids behave helps predict the outcome of their reactions and their influence on the environment they are in, valuable information in both academic and practical settings.