To determine the empirical formula of Vitamin C, we need to find the ratio of carbon, hydrogen, and oxygen atoms in the compound.
Let's start by calculating the moles of CO2 produced. The molecular weight of CO2 is 44.01 g/mol.
Number of moles of CO2 = mass of CO2 / molecular weight of CO2
Number of moles of CO2 = 1.50 g / 44.01 g/mol
Similarly, let's calculate the moles of H2O produced. The molecular weight of H2O is 18.02 g/mol.
Number of moles of H2O = mass of H2O / molecular weight of H2O
Number of moles of H2O = 0.410 g / 18.02 g/mol
Now, we can use these moles to find the moles of carbon, hydrogen, and oxygen in the compound.
Moles of carbon = 1.50 g of CO2 * (1 mol CO2 / 44.01 g CO2) * (1 mol C / 1 mol CO2)
Moles of hydrogen = 0.410 g of H2O * (1 mol H2O / 18.02 g H2O) * (2 mol H / 1 mol H2O)
Moles of oxygen = 1.50 g of CO2 * (1 mol CO2 / 44.01 g CO2) * (2 mol O / 1 mol CO2) + 0.410 g of H2O * (1 mol H2O / 18.02 g H2O) * (1 mol O / 1 mol H2O)
Now, we have the moles of carbon, hydrogen, and oxygen in the compound. We can simplify these moles by dividing each value by the smallest number to get the empirical formula.
Let's assume the smallest number of moles is for carbon.
Dividing all moles by the moles of carbon:
Moles of carbon (C) = Moles of carbon / Moles of carbon = 1
Moles of hydrogen (H) = Moles of hydrogen / Moles of carbon
Moles of oxygen (O) = Moles of oxygen / Moles of carbon
Now, we need to find the whole number ratio for the empirical formula by multiplying each value by the same factor so that the numbers become whole numbers.
The empirical formula for Vitamin C is the simplest whole number ratio of carbon, hydrogen, and oxygen atoms.
Now, the next step is determining the molecular formula of Vitamin C. The molecular formula represents the actual number of atoms of each element in one molecule of the compound.
To calculate the molecular formula, we need to know the molar mass of Vitamin C. From the given information, the molar mass of Vitamin C is 176.12 g/mol.
Now we can calculate the empirical formula mass by adding the atomic masses for the corresponding elements:
Empirical formula mass = (number of carbon atoms × atomic mass of carbon) + (number of hydrogen atoms × atomic mass of hydrogen) + (number of oxygen atoms × atomic mass of oxygen)
We can then calculate the empirical formula mass of the empirical formula obtained earlier. Let's assume the empirical formula has n carbon atoms, m hydrogen atoms, and k oxygen atoms.
Empirical formula mass = (n × 12.01 g/mol) + (m × 1.01 g/mol) + (k × 16.00 g/mol)
Finally, to determine the molecular formula, we divide the molar mass of Vitamin C by the empirical formula mass calculated earlier:
Molecular formula = Molar mass of Vitamin C / Empirical formula mass
By performing these calculations, you should be able to determine both the empirical and molecular formulas of Vitamin C.