Problem 104 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

The concentration is 2.9167 M, and the pH is approximately 0.535.

Step 1: Calculate Moles of HCl in First Solution

To find the moles of HCl in the first solution, use the formula \( moles = concentration \times volume \). Here, the volume should be in liters: \( 500 \text{ mL} = 0.5 \text{ L} \).\[moles_1 = 2.50 \, M \times 0.5 \, L = 1.25 \, moles\]

Step 2: Calculate Moles of HCl in Second Solution

Similarly, calculate the moles of HCl in the second solution using the same formula: \(\text{Volume} = 250 \text{ mL} = 0.25 \text{ L}\).\[moles_2 = 3.75 \, M \times 0.25 \, L = 0.9375 \, moles\]

Step 3: Total Moles of HCl in Mixed Solution

Add the moles of HCl from both solutions to find the total moles after mixing:\[total \: moles = 1.25 \, moles + 0.9375 \, moles = 2.1875 \, moles\]

Step 4: Calculate Concentration of HCl in Mixed Solution

To find the new concentration, divide the total moles of HCl by the total volume of the solution (after mixing, \(750 \text{ mL} = 0.75 \text{ L}\)).\[concentration = \frac{2.1875 \, moles}{0.75 \, L} = 2.9167 \, M\]

Step 5: Calculate pH of the Solution

The pH is calculated using the formula \( pH = -\log[H^+] \). Since HCl is a strong acid, its molarity is equal to the \([H^+]\) concentration.\[pH = -\log(2.9167) \approx 0.535\]

Key Concepts

Molarity

Molarity is a measure of concentration of a solution, defined as the number of moles of a solute per liter of solution. It is expressed in moles per liter (M). This measure is useful because it allows us to calculate exactly how many molecules of solute are present in a specified volume of solution. For example, in the exercise mentioned, different volumes of concentrated hydrochloric acid (HCl) solutions are mixed together.

To find the molarity of the final solution, we must first calculate the total moles of HCl present in each solution before mixing. The formula used is: \[ \text{moles} = \text{concentration} \times \text{volume} \]It's essential that the volume is always converted to liters to ensure that the units match. After determining the total moles in each solution, we sum these values to obtain the total number of moles mixed.

Finally, we determine the molarity of the mixed solution by dividing the total number of moles by the total final volume of the solution. This approach ensures that the final concentration is accurate and accounts for the dilution upon mixing.

pH Calculation

Calculating the pH of a solution helps us understand its acidity. pH is a logarithmic scale that measures the concentration of hydrogen ions \([H^+]\) in a solution. The formula for calculating pH is:\[ pH = -\log[H^+] \]Most importantly, HCl is a strong acid, meaning it completely dissociates in water. This implies that the molarity of HCl directly translates to the \([H^+]\) concentration. In our mixed solution scenario, once we calculated the molarity of 2.9167 M, this value directly contributes to the pH calculation.

By plugging 2.9167 into the formula, we get:\[ pH = -\log(2.9167) \approx 0.535 \]A pH of less than 7 indicates that the solution is acidic. The lower the pH, the more acidic the solution. As seen, a pH of around 0.535 indicates a highly acidic solution, consistent with the properties of strong acids like hydrochloric acid.

Acid-Base Reactions

Understanding acid-base reactions is crucial when dealing with solutions like HCl. These reactions involve the transfer of protons (or hydrogen ions). HCl, being a strong acid, dissociates completely in water:\[ HCl \rightarrow H^+ + Cl^- \]This indicates that hydrochloric acid readily gives up its hydrogen ions, contributing to the increase in \([H^+]\) concentration and consequently affecting the pH.

Complete dissociation is characteristic of strong acids, simplifying our calculations since we assume all the acid contributes to the hydrogen ion concentration. This reaction is a fundamental part of many chemical processes, where acids react with bases to form water and salts.

For students studying chemistry, understanding the nature of strong acids and how they interact in solutions can provide a foundation for exploring more complex biochemical reactions. Grasping these basic principles helps predict the behavior of substances during chemical reactions and is essential for accurate laboratory work.