Chemical Calculations: Formulas and Principles

Percentage Composition Calculation

To calculate the percentage composition of a compound, such as H₂O, you first determine the molecular weight of the molecule. Then, for each element, you use a conversion factor based on its contribution to the total molecular weight. This process allows you to find the percentage of each element within the compound, as shown:

Determining Empirical Formula

To calculate the empirical formula from the percentage composition of elements, follow these steps:

1. Convert the percentage of each element to grams (assuming a 100g sample).
2. Divide the mass of each element by its atomic weight to find the number of moles.
3. Divide the number of moles of each element by the smallest number of moles obtained.
4. The resulting whole numbers (or numbers close to whole numbers) represent the subscripts in the empirical formula.

These whole numbers indicate the ratio of atoms for each element in the empirical formula.

Calculating Molecular Formula

To determine the molecular formula when given the percentage composition of elements, atomic weights, and the molecular weight of the compound, you must first calculate the empirical formula. Once the empirical formula is known, calculate its empirical formula mass. Then, divide the given molecular weight by the empirical formula mass to find the integer 'n' (number of empirical formula units). The molecular formula is then the empirical formula multiplied by 'n'.

The molecular formula is derived by multiplying the subscripts of the empirical formula by this integer 'n'.

Stoichiometry and Limiting Reagents

In chemical reactions, understanding stoichiometry and identifying the limiting reagent are crucial. The limiting reagent is the reactant that is completely consumed first, thereby limiting the amount of product that can be formed. The excess reagent is the reactant that is not completely used up.

Consider the reaction: Fe₂O₃ + 3H₂O 2Fe(OH)₃

For example, if you start with 60 gr of Fe₂O₃ and 100 gr of H₂O, you would proceed to determine the limiting reagent. To determine the limiting reagent and calculate excess amounts or product formed, one typically compares the mole ratios of reactants to the stoichiometric coefficients in the balanced chemical equation. This often involves calculations similar to the following:

After performing these calculations, you can identify which reactant is the limiting reagent and which is in excess. The limiting reagent is the one that finishes first, while the excess reagent is not completely consumed.

If the problem asks for the amount of excess reagent, you would proceed to calculate the excess amount remaining:

To calculate the amount of product formed, base the calculation on the limiting reagent. To determine the amount of excess reagent remaining, subtract the amount reacted from the initial amount, as shown:

When dealing with reactions where proportions are given by mass or volume rather than molecular weights, calculations should be based on these given proportions instead of direct atomic weight divisions.

Understanding Molar Volume

Molar volume is the volume occupied by one mole of a substance. For gases at standard temperature and pressure (STP), one mole occupies approximately 22.4 liters. To calculate molar volume, you can use either the mass or volume provided. Always start with the given data (mass or volume) and use the atomic or molecular weight to perform conversions. For gases at STP, the conversion factor of 22.4 L/mol is commonly used.

Calculating the Number of Moles

The number of moles (n) of a substance can be calculated using its mass and its atomic or molecular weight. The fundamental equation is:

If you need to calculate the mass (in grams) of a substance when given the number of moles, you can rearrange and solve the same equation.

In cases where density and volume are provided, you must first calculate the mass using the density formula:

Once the mass is determined, you can then proceed to calculate the number of moles using the primary mole equation.

Avogadro's Number and Molar Conversions

Avogadro's Number is a fundamental constant in chemistry, approximately 6.022 x 10²³. It represents the number of constituent particles (atoms, molecules, ions, etc.) in one mole of a substance. It is primarily used as a conversion factor to relate the number of moles to the number of particles, or vice versa.

To convert between the number of molecules and molecular weight, or to find the number of molecules from moles, Avogadro's number is used as a conversion factor: