An unknown solid acid is either citric acid or tartaric acid. To determine which acid you have, you titrate a sample of the solid with NaOH. The appropriate reactions are as follows:

Citric acid:
H3C6H5O7 (aq) + 3NaOH (aq) -> 3H2O (l) + Na3C6H5O7 (aq)

Tartaric acid:
H2C4H4O6 (aq) + 2 NaOH (aq) -> 2H2O (l) + Na2C4H4O6

A 0.956g sample requires 29.1 mL of 0.513 M NaOH for titration to the equivalence point. What is the identity of the unknown acid?

mols base = M x L = ?

If citric acid, then mols citric acid = 1/3 mols NaOH.
If tartaric acid, then mols tartaric acid = 1/2 mols NaOH.

mols = grams/molar mass or
molar mass = grams/mols.

If citric acid then molar mass = 0.956/mols citric acid from above.
If tartaric acid then molar mass = 0.956/mols tartaric acid from above.

Look up or calculate the molar mass of both tartaric acid and citric acid and compare with the molar mass of the unknown you calculated.

To determine the identity of the unknown acid (either citric acid or tartaric acid), we can use the given information about the titration.

First, let's calculate the number of moles of NaOH used in the titration.

moles of NaOH = concentration of NaOH * volume of NaOH
= 0.513 M * 0.0291 L
= 0.0149 moles

Now, let's calculate the number of moles of acid in the sample.

For citric acid, the balanced equation tells us that 1 mole of citric acid reacts with 3 moles of NaOH, so the molar ratio is 1:3.
For tartaric acid, the balanced equation tells us that 1 mole of tartaric acid reacts with 2 moles of NaOH, so the molar ratio is 1:2.

Using the molar ratio, we can calculate the number of moles of acid in the sample for each acid.

moles of citric acid = 0.0149 moles * (1 mole citric acid / 3 moles NaOH)
= 0.00496 moles

moles of tartaric acid = 0.0149 moles * (1 mole tartaric acid / 2 moles NaOH)
= 0.00745 moles

Now, let's calculate the molar mass of the acid in the sample.

molar mass of citric acid = (mass of sample) / (moles of citric acid)
= 0.956g / 0.00496 moles
= 192.74 g/mol

molar mass of tartaric acid = (mass of sample) / (moles of tartaric acid)
= 0.956g / 0.00745 moles
= 128.47 g/mol

Comparing the molar mass calculated for each acid with their known molar masses, we can determine the identity of the unknown acid.

The molar mass of citric acid is approximately 192.74 g/mol.
The molar mass of tartaric acid is approximately 150.09 g/mol.

Based on the molar mass calculated, the unknown acid is likely tartaric acid.

Therefore, the identity of the unknown acid is tartaric acid.

To determine the identity of the unknown acid, we can use the principle of stoichiometry. By titrating the acid with NaOH, we can determine the molar ratio between the acid and NaOH and then calculate the molar mass of the acid.

First, let's find the number of moles of NaOH used in the titration:

Number of moles of NaOH = Volume of NaOH (L) × Concentration of NaOH (mol/L)

The volume of NaOH used is given as 29.1 mL, which means 29.1 mL ÷ 1000 mL/L = 0.0291 L.
The concentration of NaOH is given as 0.513 M.

Number of moles of NaOH = 0.0291 L × 0.513 mol/L = 0.0149433 mol

Next, we need to determine the molar ratio between the acid and NaOH for each acid reaction.

For citric acid:
1 mol H3C6H5O7 reacts with 3 mol NaOH

Therefore, the number of moles of citric acid present in the sample can be calculated as:

Number of moles of citric acid = (Number of moles of NaOH) ÷ 3 = 0.0149433 mol ÷ 3 = 0.0049811 mol

For tartaric acid:
1 mol H2C4H4O6 reacts with 2 mol NaOH

Therefore, the number of moles of tartaric acid present in the sample can be calculated as:

Number of moles of tartaric acid = (Number of moles of NaOH) ÷ 2 = 0.0149433 mol ÷ 2 = 0.00747165 mol

Now, we can calculate the molar mass of each acid by dividing the given mass of the sample by the corresponding number of moles calculated above.

For citric acid:
Molar mass of citric acid = Mass of sample ÷ Number of moles of citric acid
= 0.956 g ÷ 0.0049811 mol = 192.03 g/mol

For tartaric acid:
Molar mass of tartaric acid = Mass of sample ÷ Number of moles of tartaric acid
= 0.956 g ÷ 0.00747165 mol = 128.00 g/mol

Comparing the molar masses calculated, we find that the molar mass of citric acid (192.03 g/mol) is higher than that of tartaric acid (128.00 g/mol).

Therefore, based on the molar mass, the identity of the unknown acid is citric acid.