Ascorbic acid (vitamin C) is a diprotic acid having the formula H2C6H6O6. A sample of a vitamin supplement was analyzed by titrating a 0.3252 g sample dissolved in water with 0.0284 M NaOH. A volume of 13.27 mL of the base was required to completely neutralize the ascorbic acid. What was the percentage by mass of ascorbic acid in the sample?
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To find the percentage by mass of ascorbic acid in the sample, you need to determine the number of moles of ascorbic acid and then calculate its mass.
First, calculate the number of moles of NaOH used in the titration:
Moles of NaOH = Volume of NaOH (in liters) × Molarity of NaOH
= 13.27 mL × (1 L / 1000 mL) × 0.0284 mol/L
= 0.000377 mol
Since NaOH reacts with ascorbic acid in a 1:1 ratio, the moles of ascorbic acid in the sample can be determined as:
Moles of ascorbic acid = Moles of NaOH
= 0.000377 mol
Now, find the molar mass of ascorbic acid:
Molar mass of ascorbic acid (H₂C₆H₆O₆) = 2(1.01 g/mol) + 6(12.01 g/mol) + 6(1.01 g/mol) + 6(16.00 g/mol)
= 176.12 g/mol
Calculate the mass of ascorbic acid in the sample:
Mass of ascorbic acid = Moles of ascorbic acid × Molar mass of ascorbic acid
= 0.000377 mol × 176.12 g/mol
= 0.0667 g
Finally, calculate the percentage by mass of ascorbic acid:
Percentage by mass = (Mass of ascorbic acid / Mass of sample) × 100%
= (0.0667 g / 0.3252 g) × 100%
= 20.53%
Therefore, the percentage by mass of ascorbic acid in the sample is approximately 20.53%.