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Chapter 4: Problem 151

Citric acid, which can be obtained from lemon juice, has the molecular formula \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) . A 0.250 -g sample of citric acid dissolved in 25.0 mL of water requires 37.2 mL of 0.105 M NaOH for complete neutralization. What number of acidic hydrogens per molecule does citric acid have?

Short Answer

Expert verified
Citric acid has 3 acidic hydrogens per molecule.

Step by step solution

01

Calculate the moles of NaOH used

To find the number of acidic hydrogens in citric acid, we first need to determine the moles of NaOH used in the neutralization reaction. The given information is the volume of NaOH, 37.2 mL, and its concentration, 0.105 M. We can use the formula \(moles = (volume \cdot concentration)\) to determine the moles of NaOH: \(moles_{NaOH} = volume_{NaOH} \cdot concentration_{NaOH}\)
02

Convert mL to L

Before calculating the moles of NaOH, we need to convert the volume from mL to L: \(volume_{NaOH} (L) = 37.2 \, \text{mL} \cdot \frac{1\, \text{L}}{1000\, \text{mL}} = 0.0372\, \text{L}\)
03

Calculate moles of NaOH

Now we can calculate the moles of NaOH used in the reaction: \(moles_{NaOH} = 0.0372\, \text{L} \cdot 0.105\, \text{M} = 0.003906\, \text{moles}\)
04

Find moles of citric acid

Since each molecule of citric acid will react with an integer number of NaOH molecules, we can start by assuming a 1:1 mole ratio between citric acid and the acidic hydrogens, and see if it is true. If not, we will continue with higher ratios. First, determine the moles of citric acid in the provided sample. Given sample mass is 0.250 g. Use the molar mass of citric acid, which can be calculated from the molecular formula: \(Molar \, mass_{citric \, acid} = 6 \cdot 12.01 + 8 \cdot 1.01 + 7 \cdot 16 = 192.12\, \text{g/mol}\) Determine the moles of citric acid by dividing the mass by the molar mass: \(moles_{citric \, acid} = \frac{0.250\, \text{g}}{192.12\, \text{g/mol}} = 0.001301\, \text{moles}\)
05

Determine the ratio between moles of NaOH and citric acid

Now we will compare the moles of NaOH with the moles of citric acid to determine the ratio between them: \(ratio = \frac{moles_{NaOH}}{moles_{citric \, acid}} = \frac{0.003906}{0.001301} \approx 3\)
06

Determine the number of acidic hydrogens per citric acid molecule

The ratio of approximately 3 indicates that each citric acid molecule has 3 acidic hydrogen atoms. Therefore, citric acid has 3 acidic hydrogens per molecule.

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