Chapter 15: Problem 61

A 50 \(\mathrm{mL}\) sample of apple juice has a pH of \(3.2 .\) What amount, in moles, of \(\mathrm{H}_{3} \mathrm{O}^{+}\) is present?

Short Answer

Expert verified

The amount of \(\mathrm{H}_{3} \mathrm{O}^{+}\) present in the apple juice sample is \(10^{-3.2} * 0.05\) moles.

Step by step solution

Calculate the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)

Firstly, use the definition of pH \([- \log [\mathrm{H}_{3} \mathrm{O}^{+}]\ = pH\] to calculate the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\). Rearrange the formula and apply the given pH value of 3.2: \([\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-pH} = 10^{-3.2}\).

Convert the volume in liters

The volume in the given problem is in milliliters, so this needs to be converted to liters, as the formula for calculating the amount in moles uses liters. This is done by dividing the given volume by 1000: \(volume = \frac{50}{1000} = 0.05 L\).

Calculate the amount in moles

Now, use the formula \([\text{concentration} = \frac{\text{amount in moles}}{\text{volume in liters}}]\) and rearrange it for the amount in moles: \(\text{amount in moles} = \text{concentration} * \text{volume in liters}\). Substituting the calculated concentration and volume into this formula leads to: \(\text{amount in moles} = 10^{-3.2} * 0.05\).

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A 50 \(\mathrm{mL}\) sample of apple juice has a pH of \(3.2 .\) What amount, in moles, of \(\mathrm{H}_{3} \mathrm{O}^{+}\) is present?

Short Answer

Step by step solution

Calculate the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\)

Convert the volume in liters

Calculate the amount in moles

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