Question

Formic acid is partly responsible for the sting of ant bites. By mass, formic acid is \(26.10 \% \mathrm{C}, 4.38 \% \mathrm{H},\) and 69.5\(\%\) O.The molar mass of formic acid is 46.02 \(\mathrm{g} / \mathrm{mol} .\) Find the molecular formula of formic acid and draw its Lewis structure.

Short answer

The molecular formula of formic acid is CH2O2. The Lewis structure shows a carbon atom double-bonded to an oxygen atom (carbonyl group) and single-bonded to another oxygen atom, which in turn is bonded to a hydrogen atom (carboxyl group).

Step-by-step solution

- Calculate moles of elements per 100g formic acid

Assume a 100g sample of formic acid. Therefore, we have 26.10g of C, 4.38g of H, and 69.52g of O. Calculate the moles of each element by dividing their mass by their atomic masses: C (12.01g/mol), H (1.008g/mol), and O (16.00g/mol).

- Determine the simplest mole ratio

Divide the moles of each element by the smallest number of moles calculated in Step 1 to get the simplest whole number ratio.

- Predict empirical formula

The empirical formula is determined by the smallest whole number ratios of moles of elements. Multiply mole ratios if necessary to get whole numbers.

- Determine the molecular formula using the molar mass

Multiply the empirical formula by an integer factor so that the empirical formula mass multiplied by this factor equals the molar mass of formic acid (46.02 g/mol).

- Draw the Lewis structure

Draw the Lewis structure for formic acid by arranging the atoms and distributing the valence electrons to satisfy the octet rule for carbon and oxygen, and duet rule for hydrogen.

Key concepts

Empirical Formula Calculation

When attempting to understand the makeup of a compound, the empirical formula serves as an essential first step. It represents the simplest whole number ratio of the elements within a molecule. It does not, however, provide the exact number of atoms, but it is a crucial piece in the puzzle of molecular composition. To calculate the empirical formula from a given percentage composition, one typically assumes a 100 g sample, which converts percentages into grams directly.

For instance, if formic acid has 26.10% carbon, 4.38% hydrogen, and 69.52% oxygen, you would have 26.10 g of carbon, 4.38 g of hydrogen, and 69.52 g of oxygen in a 100 g sample. To find the moles of each element, divide these masses by the respective atomic masses: carbon (12.01 g/mol), hydrogen (1.008 g/mol), and oxygen (16.00 g/mol). The smallest number of moles calculated then becomes the reference to determine the simplest mole ratio.

You divide the moles of each individual element by this smallest value to achieve a mole ratio that ideally reflects whole numbers. If the ratio does not produce whole numbers, it can be multiplied by a suitable factor to achieve them. This mole ratio then provides the empirical formula of the compound, which is a pivotal step in molecular analysis and further chemical understanding.

Mole Concept in Chemistry

The mole concept in chemistry is fundamental to quantifying the number of particles in a substances. Avogadro's number, which is approximately 6.022 x 10²³, allows chemists to count atoms and molecules in a way that corresponds with their atomic or molecular weights in grams. This gives the molar mass, the mass of one mole of a substance, and effectively connects the microscopic world of atoms to macroscopic quantities that can be measured.

In practical terms, the molar mass tells us how many grams are in one mole of a substance, making it possible to convert between mass and moles. This is instrumental in empirical formula calculations where the mass of each element in a compound is measured or given, and from which the number of moles can be determined. The molar mass is also key in finding the molecular formula from the empirical formula, allowing us to compare the empirical formula mass to the molar mass of the compound to find out how many empirical units make up the actual molecule.

Lewis Structure Representation

Lewis structures are visual representations that show how atoms in a molecule are bonded together and how the valence electrons are distributed among them. To draw a Lewis structure, one starts by counting the total number of valence electrons for all the atoms present. This total is crucial for determining how electrons are shared or paired to form bonds, in adherence with the octet rule for most atoms and the duet rule for hydrogen.

When drawing the Lewis structure of formic acid, for instance, carbon is the central atom, typically bonded to other elements. Hydrogen atoms are usually placed on the outside, and oxygen may form double bonds if needed to achieve a stable configuration. Electrons are represented as dots or lines (representing shared pairs), indicating bonds between atoms. Lewis structures provide a two-dimensional way to visualize the three-dimensional shape of molecules and help predict the types of chemical reactions that compounds may undergo.