Question

The concentration of hydrogen ions in a sample of soft drink is \( 2\times10^{-4}\,\text{mol L}^{-1} \). Its pH value is ( \( \log 2 = 0.3010 \) )

• A. \(4.369 \)
• B. \(3.699 \)
• C. \(2.369 \)
• D. \(5.301 \)
• E. \(3.301 \)

Hint:

\(\log(ab) = \log a + \log b\)

Answer 1

The Correct Option is B

Step 1: Understanding pH:
pH is a measure of the acidity or alkalinity of a solution. It is defined as the negative base-10 logarithm of the hydrogen ion concentration [H\(^+\)].
Step 2: Key Formula or Approach:
The formula to calculate pH is:
\[ \text{pH} = -\log_{10}[\text{H}^+] \] where [H\(^+\)] is the molar concentration of hydrogen ions.
Step 3: Detailed Calculation:
We are given the hydrogen ion concentration:
\[ [\text{H}^+] = 2 \times 10^{-4} \text{ mol/L} \] Substitute this value into the pH formula:
\[ \text{pH} = -\log_{10}(2 \times 10^{-4}) \] Using the logarithm property \(\log(a \times b) = \log(a) + \log(b)\):
\[ \text{pH} = -(\log_{10}(2) + \log_{10}(10^{-4})) \] Using the logarithm property \(\log(10^x) = x\):
\[ \text{pH} = -(\log_{10}(2) - 4) \] Now, distribute the negative sign:
\[ \text{pH} = 4 - \log_{10}(2) \] We are given that \(\log_{10}(2) = 0.3010\).
\[ \text{pH} = 4 - 0.3010 \] \[ \text{pH} = 3.699 \] Step 4: Final Answer:
The pH value of the soft drink sample is 3.699.