Question

Maleic acid is an organic compound composed of $41.39\mathrm{\%}$ C, $3.47\mathrm{\%}$ H, and the rest oxygen. If 0.129 mole of maleic acid has a mass of $15.0\mathrm{g},$ what are the empirical and molecular formulas of maleic acid?

Short answer

The empirical formula for maleic acid is $C_2{H}_2{O}_2$, and the molecular formula is $C_4{H}_2{O}_4$.

Step-by-step solution

Calculate moles of each element from their percentages

Divide the percentage composition by the molar mass of each element: $molesofCarbon=\frac{41.39\mathrm{\%}}{12.01g/mol}$ $molesofHydrogen=\frac{3.47\mathrm{\%}}{1.01g/mol}$ $ moles\ of\ Oxygen = 100\% - 41.39\% - 3.47\% = 55.14\% $, then divide by its molar mass: $molesofOxygen=\frac{55.14\mathrm{\%}}{16.00g/mol}$

Convert percentages to simplest whole number ratios

To find the simplest whole number ratio of moles, divide each amount by the smallest mole value: $C:\frac{41.39/12.01}{3.47/1.01}=2$ $H:\frac{3.47/1.01}{3.47/1.01}=1$ $O:\frac{55.14/16.00}{3.47/1.01}=2$ So the empirical formula is: $C_2{H}_2{O}_2$

Calculate molar mass of empirical formula

Find the molar mass of the empirical formula $C_2{H}_2{O}_2$ by adding together the molar masses of its constituent elements: $Molarmassof{C}_2{H}_2{O}_2=2(12.01g/mol)+2(1.01g/mol)+2(16.00g/mol)=58.04g/mol$

Calculate molar mass of the molecular formula

We know the mass of 0.129 moles of maleic acid is 15.0 grams. So the molar mass of the molecular formula is: $Molarmassofmolecularformula=\frac{15.0g}{0.129mol}=116.28g/mol$

Determine molecular formula

Divide the molar mass of the molecular formula by the molar mass of the empirical formula to find the ratio (n) of the molecular formula to the empirical formula: $n=\frac{116.28g/mol}{58.04g/mol}=2$ Thus, the molecular formula is: $C_{2(2)}{H}_{2(1)}{O}_{2(2)}=C_4{H}_2{O}_4$ The empirical formula for maleic acid is $C_2{H}_2{O}_2$, and the molecular formula is $C_4{H}_2{O}_4$.

Key concepts

Empirical Formula

The empirical formula in chemistry is the simplest representation of a compound. It shows the relative number of each type of atom in the molecule, but not the exact number found in the actual molecule. To find it, we use percentage composition data. From the example exercise, maleic acid has a unique composition of carbon, hydrogen, and oxygen. By dividing the percentage of each element by its atomic mass, you determine its number of moles.

After that, you convert these mole values into whole numbers to find the simplest ratio. In maleic acid's case, the empirical formula is derived as $C_2{H}_2{O}_2$ by calculating the simplest ratio of moles: 2 moles of carbon to 1 mole of hydrogen to 2 moles of oxygen. This gives us a fundamental insight into the proportions of atoms making up maleic acid.

Molecular Formula

The molecular formula describes the exact number of each type of atom in a molecule. It expands on the empirical formula and provides more precise information about the molecular structure. In the exercise, after determining the empirical formula $C_2{H}_2{O}_2$, the molar mass of the empirical formula is calculated. For maleic acid, it is $58.04g/mol$.

Since we also know that 15.0 grams of maleic acid is equal to 0.129 moles, we calculate the molar mass of maleic acid by dividing: $\frac{15.0g}{0.129mol}=116.28g/mol$. By comparing this molar mass with that of the empirical formula, you determine the multiple of the empirical formula units in the molecular formula, which is 2 in this case.

The molecular formula of maleic acid is $C_4{H}_2{O}_4$, indicating exactly 4 carbons, 2 hydrogens, and 4 oxygens per molecule.

Percentage Composition

Understanding the percentage composition is crucial in determining the empirical formula. It provides a breakdown of how much each element contributes to the total mass of a compound. In our example, maleic acid is made up of $41.39\mathrm{\%}$ carbon, $3.47\mathrm{\%}$ hydrogen, and the remaining $55.14\mathrm{\%}$ is oxygen.

This data provides the necessary information to calculate the moles of each element by dividing the percentage by the element's atomic mass. This step is an essential part of finding the simplest ratio of elements in the compound, which ultimately leads to the empirical formula. It's like peeling an onion layer by layer to see what truly makes up the substance.

Maleic Acid

Maleic acid is an important organic compound in chemistry, often used to study structural and compositional aspects. It's isomeric with fumaric acid but has distinct properties due to its unique configuration of atoms. In practice, understanding maleic acid's composition helps in comprehending concepts like isomerism and acid behavior.

The composition used in our exercise — carbon, hydrogen, and oxygen percentages — is often a starting point in unraveling its formula. Describing how these percentages translate into molecular structure involves empirical and molecular formulas, which paint a vivid picture of maleic acid's composition.

Complex compounds like maleic acid underscore the necessity of mastering empirical and molecular formula calculations, which are crucial tools in organic chemistry.