Question

A student is given \(0.930 \mathrm{~g}\) of an unknown acid, which can be either oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) or citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\). To determine which acid she has, she titrates the unknown acid with \(0.615 \mathrm{M} \mathrm{NaOH}\). The equivalence point is reached when \(33.6 \mathrm{~mL}\) are added. What is the unknown acid?

Short answer

Answer: The unknown acid is most likely oxalic acid.

Step-by-step solution

Calculate moles of NaOH used in titration

First, we want to know how many moles of NaOH were used to reach the equivalence point. We do this by multiplying the concentration of NaOH by the volume of NaOH used in the titration: moles of NaOH = concentration of NaOH * volume of NaOH moles of NaOH = 0.615 M * 33.6 mL * (1 L/1000 mL) moles of NaOH = 0.0207 mol

Determine the moles of the unknown acid using mole ratios

Since the unknown acid is either oxalic acid (H2C2O4) or citric acid (H3C6H5O7), we will consider two possible mole ratios for the reaction with NaOH (1:2 and 1:3, respectively). For oxalic acid (1:2): moles of unknown acid = moles of NaOH / 2 moles of unknown acid = 0.0207 mol / 2 moles of unknown acid = 0.01035 mol For citric acid (1:3): moles of unknown acid = moles of NaOH / 3 moles of unknown acid = 0.0207 mol / 3 moles of unknown acid = 0.0069 mol

Calculate the experimental molar mass of the unknown acid

Next, we will calculate the experimental molar mass of the unknown acid, using the given mass of the acid (0.930 g), and the moles calculated in Step 2. For oxalic acid: experimental molar mass = mass / moles experimental molar mass = 0.930 g / 0.01035 mol experimental molar mass = 89.9 g/mol For citric acid: experimental molar mass = mass / moles experimental molar mass = 0.930 g / 0.0069 mol experimental molar mass = 134.8 g/mol

Compare the experimental molar mass with the known molar masses of oxalic acid and citric acid

Now, we will compare the calculated experimental molar masses of the unknown acid with the known molar masses of oxalic acid (90.03 g/mol) and citric acid (192.12 g/mol). For oxalic acid: Difference in molar mass = |89.9 g/mol - 90.03 g/mol| Difference in molar mass = 0.13 g/mol For citric acid: Difference in molar mass = |134.8 g/mol - 192.12 g/mol| Difference in molar mass = 57.32 g/mol

Identify the unknown acid

Comparing the difference between the experimental and known molar masses, we can conclude that since the difference for oxalic acid (0.13 g/mol) is much smaller than the difference for citric acid (57.32 g/mol), the unknown acid is most likely oxalic acid (H2C2O4).