Question

Fructose is a common sugar found in fruit. Elemental analysis of fructose gives the following mass percent composition: \(\mathrm{C} 40.00 \%, \mathrm{H}\) \(6.72 \%, \mathrm{O} 53.28 \% .\) The molar mass of fructose is 180.16 \(\mathrm{g} / \mathrm{mol} .\) Find the molecular formula of fructose.

Short answer

The molecular formula of fructose is \(C_6H_{12}O_6\).

Step-by-step solution

Determine Moles of Each Element Per 100 g of Fructose

Since the mass percent composition is given, assume a 100 g sample of fructose. This means there are 40.00 g of carbon (C), 6.72 g of hydrogen (H), and 53.28 g of oxygen (O). Calculate moles of each element by dividing the mass of each element by its atomic mass (C: about 12.01 g/mol, H: about 1.008 g/mol, O: about 16.00 g/mol).

Find the Simplest Mole Ratio

Divide the number of moles of each element by the smallest number of moles from Step 1. This will give the simplest whole number ratio between the elements.

Determine Empirical Formula

Use the simplest mole ratio to write the empirical formula. If the ratio is not a whole number, multiply the subscripts by the smallest number that will convert them all to whole numbers.

Calculate the Molar Mass of the Empirical Formula

Add up the atomic masses of all the atoms in the empirical formula to find its molar mass.

Divide the Molar Mass of Fructose by the Molar Mass of the Empirical Formula

Divide the molar mass of fructose (180.16 g/mol) by the molar mass of the empirical formula to find the ratio of the molecular formula to the empirical formula.

Determine the Molecular Formula

Multiply the subscripts in the empirical formula by the ratio found in Step 5 to get the molecular formula.

Key concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. It is based on the relative number of atoms of each type in the compound, not necessarily on the actual number of atoms present. To determine the empirical formula, one must first convert the mass percent composition into moles, using the atomic masses of each element. Next, the moles are divided by the smallest number to find the simplest mole ratio.

For example, if we have a compound with 40.00% carbon, 6.72% hydrogen, and 53.28% oxygen, by assuming a 100 g sample, these percentages convert directly to grams. Dividing each element's mass by its atomic mass gives us the number of moles. The smallest mole amount is then used to divide all mole amounts to get the simplest ratio. Occasionally, this ratio might not be perfect whole numbers, and in such cases, it's necessary to multiply all ratios by a common factor to achieve whole-number subscripts.

Mass Percent Composition

Mass percent composition reveals the percentage by mass of each element within a compound. Knowing the mass percent composition is crucial for determining the empirical formula. This percentage is calculated by taking the mass of each element in a sample and dividing it by the total mass of the sample, then multiplying by 100.

For instance, if fructose has mass percent compositions of 40.00% for Carbon, 6.72% for Hydrogen, and 53.28% for Oxygen, these values imply that in every 100 grams of fructose, there are 40 grams of carbon, 6.72 grams of hydrogen, and 53.28 grams of oxygen. To find the empirical formula, students convert these mass percentages to moles, which is a manageable step as the composition is already given per 100 grams of the substance.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is the sum of the atomic masses of all atoms in a chemical formula and is important for converting between grams and moles. To determine the molar mass, we take the atomic mass of each element, as found on the periodic table, and multiply by the number of times this element appears in the compound's formula.

In the case of fructose, the molar mass is given as 180.16 g/mol. This molar mass acts as a conversion factor between grams and moles, which is essential in various calculations, including stoichiometry and determining the molecular formula from the empirical formula.

Stoichiometry

Stoichiometry is the study of the quantitative relationships, or ratios, between reactants and products in chemical reactions. It is based on the conservation of mass and the concept of moles. Stoichiometry calculations involve using the balanced chemical equation to determine the amount of reactants needed or the amount of products formed.

In the context of finding a compound's molecular formula, stoichiometry allows us to relate the empirical formula mass to the actual molar mass of the compound. By dividing the compound's molar mass by the empirical formula mass, we find the ratio necessary to scale up the empirical formula to its molecular counterpart—thereby revealing the true number of atoms in a single molecule of the compound.