8. Ascorbic acid (Vitamin C) cannot be stored in the body, so it must be supplied in the diet. It is a C, H, O compound. If 7.75 g of Vitamin C is combusted in excess oxygen, it yields 11.62 g of CO2 and 3.17 g of water. The molar mass of Vitamin C lies between 150 and 200 g/mole. Determine its molecular formula.

Molecular formula = C6H8O6

The molar mass of vitamin C = 176.14 g/mol

Explanation:

Step 1: Data given

Mass of vitamin C = 7.75 grams

Mass of CO2 = 11.62 grams

Mass of H2O = 3.17 grams

Molar mass of CO2 = 44.01 g/mol

Molar mass of H2O = 18.02 g/mol

Molar mass C = 12.01 g/mol

Molar mass H = 1.01 g/mol

Molar mass O = 16.0 g/mol

Step 2: Calculate moles CO2

Moles CO2 = 11.62 grams / 44.01 g/mol

Moles CO2 = 0.264 moles

Step 3: Calculate moles C

For 1 mol CO2 we have 1 mol C

For 0.264 moles CO2 we have 0.264 moles

Step 4: Calculate mass C

Mass C = 0.264 moles * 12.01 g/mol

Mass C = 3.17 grams

Step 5: Calculate moles H2O

Moles H2O = 3.17 grams / 18.02 g/mol

Moles H2O = 0.176 moles

Step 6: Calculate moles H

For 1 mol H2O we have 2 moles H

For 0.176 moles H2O we have 2*0.176 = 0.352 moles

Step 6: Calculate mass H

Mass H = 0.352 moles * 1.01 g/mol

Mass H = 0.356 grams

Step 7: Calculate mass O

Mass O = 7.75 grams - 3.17 - 0.356

Mass O = 4.224 grams

Step 8: Calculate moles O

Mass O = 4.224 grams / 16.0 g/mol

Mass O = 0.264 moles

Step 9: Calculate mol ratio

We divide by the smallest amount of moles

C: 0.264 moles / 0.264 moles = 1

H: 0.352 moles / 0.264 moles = 1.33

O: 0.264 moles / 0.264 moles = 1

This means for each C atom we have 1.33 H atoms and 1 O atom

OR

For every 3 C atoms we have 4 H atoms and 3 O atoms

The empirical formula is C3H4O3

Step 10: Calculate the molecular formula

The molecular mass of the empirical formula is 88.07

Since the molar mass of vitamin C is between 150 and 200 g/mol

We have to multiply the empirical formula by 2

Molecular formula = 2 * (C3H4O3) = C6H8O6

The molar mass of vitamin C = 176.14 g/mol