Question

The \(\mathrm{pH}\) of a solution produced when an aqueous solution of strong acid \(\mathrm{pH} 5\) mixed with equal volume of an aqueous solution of strong acid of \(\mathrm{pH} 3\) is (1) \(3.3\) (2) \(3.5\) (3) \(4.5\) (4) \(4.0\)

Short answer

Option (1): 3.3

Step-by-step solution

Determine the Hydrogen Ion Concentration of Each Solution

The \(\text{pH}\) of a solution is given by the formula \[ \text{pH} = -\text{log}[\text{H}^+] \] From this, we can determine \([\text{H}^+]\text{ in Solution 1}\) and \([\text{H}^+]\text{ in Solution 2}\) using \[ [\text{H}^+] = 10^{-\text{pH}} \] For Solution 1: \(\text{pH} = 5\), so \[ [\text{H}^+]_{1} = 10^{-5} \] For Solution 2: \(\text{pH} = 3\), so \[ [\text{H}^+]_{2} = 10^{-3} \]

Compute the Total Hydrogen Ion Concentration

When equal volumes of the two solutions are mixed, the total hydrogen ion concentration is the average of the concentrations: \[ [\text{H}^+]_{\text{total}} = \frac{[\text{H}^+]_{1} + [\text{H}^+]_{2}}{2} \] Substituting the values obtained in Step 1: \[ [\text{H}^+]_{\text{total}} = \frac{10^{-5} + 10^{-3}}{2} = \frac{0.00001 + 0.001}{2} = \frac{0.00101}{2} = 0.000505 \]

Determine the pH of the Mixed Solution

Now use the hydrogen ion concentration to find the \(\text{pH}\): \[ \text{pH} = -\text{log}[\text{H}^+]_{\text{total}} \] Substituting \[ [\text{H}^+]_{\text{total}} = 0.000505 \] \[ \text{pH} = -\text{log}(0.000505) \approx 3.3 \]

Key concepts

pH Formula

The pH formula is a crucial concept in chemistry. It helps us measure the acidity or basicity of a solution. The formula to calculate pH is given by:
\( \text{pH} = - \text{log}[\text{H}^+] \).
The \( [\text{H}^+] \) refers to the hydrogen ion concentration in the solution. Using the logarithm base 10, the pH value tells us how acidic or basic a solution is.
Lower pH values correspond to higher acidity whereas higher values indicate higher basicity. For example, a solution with a pH of 3 is more acidic than a solution with a pH of 5.
Remember, even small changes in pH represent significant changes in hydrogen ion concentration, since the pH scale is logarithmic.

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration \([\text{H}^+]\) is essential for pH calculations. This represents how many hydrogen ions are present in a certain volume of solution.
To find \( [\text{H}^+] \), you can use the formula:
\([\text{H}^+] = 10^{-\text{pH}} \)
For example, if the pH of a solution is 5, the hydrogen ion concentration \( [\text{H}^+] \) would be \( 10^{-5} \). If the pH is 3, \([\text{H}^+] \) would be \( 10^{-3} \).
A higher hydrogen ion concentration (lower pH) indicates a more acidic solution, while a lower hydrogen ion concentration (higher pH) indicates a more basic solution.

Strong Acid Mixture

Mixing strong acids involves understanding how their hydrogen ion concentrations combine. When you mix two solutions of equal volume, the resulting hydrogen ion concentration is the average of the two.
For example, if one solution has a pH of 5 and another has a pH of 3, the concentrations would be \([\text{H}^+]_1 = 10^{-5} \) and \([\text{H}^+]_2 = 10^{-3} \).
When mixed in equal volumes, the average hydrogen ion concentration \( [\text{H}^+]_{\text{total}} \) is calculated as:
\( [\text{H}^+]_{\text{total}} = \frac{10^{-5} + 10^{-3}}{2} = \frac{0.00001 + 0.001}{2} = 0.000505 \).
Finally, to find the pH of the mixed solution, use the formula:
\( \text{pH} = - \text{log}(0.000505) \), which approximately equals 3.3.
This result shows how the pH of the mixture is influenced by the stronger acid (lower pH value) due to its higher hydrogen ion concentration.