Question 42 of 69beginner🔧 ApplyNumerical1 mark

The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.

Correct Answer

The concentration of hydrogen ion in the vinegar sample is 1.74×10−41.74 \times 10^{-4} M.

Exercise: EXERCISES | Q: 6.42 | (Page 45)
For More Understanding

Explanation

The relationship between pH and hydrogen ion concentration is given by pH=−log⁡[H+]\text{pH} = -\log[\text{H}^+]. To find the hydrogen ion concentration from a given pH value, we rearrange the formula to [H+]=10−pH[\text{H}^+] = 10^{-\text{pH}} or take the antilog of the negative pH.

Solution Steps

  1. Step 1: Write the formula relating pH and hydrogen ion concentration: pH=−log⁡[H+]\text{pH} = -\log[\text{H}^+].

  2. Step 2: Substitute the given pH value of the vinegar sample: 3.76=−log⁡[H+]3.76 = -\log[\text{H}^+].

  3. Step 3: Rearrange the equation to solve for log⁡[H+]\log[\text{H}^+]: log⁡[H+]=−3.76\log[\text{H}^+] = -3.76.

  4. Step 4: Express the negative value in characteristic and mantissa form for antilog calculation: log⁡[H+]=4‾.24\log[\text{H}^+] = \overline{4}.24.

  5. Step 5: Take the antilog to find the hydrogen ion concentration: [H+]=1.74×10−4[\text{H}^+] = 1.74 \times 10^{-4} M.

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