Question

The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it in \(\text{mol dm}^{-3}\) ?

• A. \(1.97 \times 10^{-4}\)
• B. \(1.738 \times 10^{-4}\)
• C. \(1.84 \times 10^{-4}\)
• D. \(1.283 \times 10^{-4}\)

Hint:

Split powers: \(10^{-3.76} = 10^{-4} \times 10^{0.24}\) for faster calculation.

Answer 1

The Correct Option is B

Concept:
pH is defined as: \[ \text{pH} = -\log [\text{H}^+] \] Step 1: Rearrange the formula. \[ [\text{H}^+] = 10^{-\text{pH}} \]
Step 2: Substitute the given value. \[ [\text{H}^+] = 10^{-3.76} \]
Step 3: Evaluate using logarithm rules. \[ 10^{-3.76} = 10^{-4} \times 10^{0.24} \] \[ 10^{0.24} \approx 1.738 \] \[ [\text{H}^+] = 1.738 \times 10^{-4} \]
Step 4: Conclusion. \[ [\text{H}^+] = 1.738 \times 10^{-4}\text{ mol dm}^{-3} \]