Question

Conc. of H ions in HCl solution is \( 3\times 10^{-3}\text{M} \) then pH = -------?

Hint:

A quick way to estimate pH for an ion concentration of \( A \times 10^{-B} \) is to use the formula \( \text{pH} = B - \log(A) \).
Memorizing basic log values like \( \log(2) \approx 0.30 \) and \( \log(3) \approx 0.48 \) will save you calculation time during the exam.

Answer 1

Step 1: Understanding the Concept:
The pH of a solution is a measure of its acidity, mathematically defined as the negative base-10 logarithm of the hydrogen ion concentration.
Step 2: Key Formula or Approach:
The formula used is:
\[ \text{pH} = -\log_{10}[\text{H}^+] \] Step 3: Detailed Explanation:
We are given that the concentration of hydrogen ions \( [\text{H}^+] \) is \( 3 \times 10^{-3} \text{ M} \).
Substitute the given value directly into the pH formula:
\[ \text{pH} = -\log_{10}(3 \times 10^{-3}) \] Using the logarithmic property \( \log(a \times b) = \log(a) + \log(b) \):
\[ \text{pH} = -(\log_{10}(3) + \log_{10}(10^{-3})) \] We know that \( \log_{10}(10^{-3}) = -3 \) and the standard accepted value for \( \log_{10}(3) \approx 0.4771 \).
\[ \text{pH} = -(0.4771 - 3) \] \[ \text{pH} = 3 - 0.4771 \] \[ \text{pH} = 2.5229 \] Rounding to two decimal places, the calculated pH is 2.52.
Step 4: Final Answer:
The pH of the solution is 2.52.