The student is expected to perform stoichiometric calculations, including determination of mass relationships between reactants and products, calculation of limiting reagents, and percent yield.
Stoichiometry is the portion of chemistry dealing with numerical relationships in chemical reactions, where conversion factors such as “per expressions”, or ratios, are used to determine the mass relationships between reactants and products. Mole ratios are used to determine the relationships among moles of various compounds in a reaction, and these ratios can be determined from the coefficients of a balanced chemical equation. The molar masses of reactants and products are used as conversion factors to calculate mass relationships.
A limiting reagent is the reactant that determines the amount of product formed in a reaction, as it is the reactant that is completely consumed first. When one of the reactants is consumed in a chemical reaction, the reaction stops and no further products may be formed. To calculate the limiting reactant, use stoichiometry to determine which reactant is consumed first, and then use the amount of this reactant to find the moles or mass of product formed.
Stoichiometry can be used to find the theoretical yield of a chemical, the quantity that shows the theoretical amount of product that could be produced in an ideal chemical reaction in which there is a complete conversion of reactant(s) to product(s). The actual yield is a measured quantity of the actual amount of product produced during a chemical reaction. The percent yield of a reaction is found by dividing the actual amount of a product by the theoretical amount of the product, and then multiplying by 100 to make a percent.
Importance of Numerical Relationships in Chemistry
In Greek, stoikhein means “element” and metron means “measure,” so stoichiometry literally translated means the “measure of elements.” Stoichiometry is the culmination of many concepts in chemistry. It integrates dimensional analysis, moles and molar mass, molar volumes of gases, concentrations, and balanced chemical equations. Stoichiometry allows the use of information about one compound in a reaction to determine the information of another compound in the same reaction.
Dimensional Analysis
The method known as dimensional analysis uses conversion factors, often called “per expressions” (ratios), to determine several different types of relationships between reactants and products. One common conversion factor used in dimensional analysis is molar mass, which refers to the mass of one mole of a substance. It is written as grams per mole, or g/mol. Every chemical reaction has its own characteristic proportions, and these proportions are used as conversion factors to solve stoichiometric problems. The major function of stoichiometry is the method of using these proportions to obtain chemical formulas, equations, atomic masses, and molecular masses. Stoichiometry allows scientists to calculate what is used in chemical reactions, and how much is used or produced during chemical processes.
Stoichiometric Coefficients
To balance an equation, it is necessary that there are the same number of atoms on the left side of the equation as the right. One can do this by raising the coefficients. The stoichiometric coefficient is the number written in front of atoms, ions, and molecules in a chemical reaction to balance the number of each element on both the reactant and product sides of the equation. Stoichiometric coefficients should be represented with whole numbers. Stoichiometric coefficients are useful as they establish the mole ratio between the reactants and products of a chemical reaction.
Mole Ratios
Each element has its own atomic mass, which is the same as the element’s molar mass. When atoms combine into compounds, each compound will then have its own molar mass. As stated earlier, these molar masses are represented as g/mol. This is one conversion factor used in stoichiometry. Another common proportion used in stoichiometry has to do with the number of particles contained within a sample. According to Avogadro’s constant, there are 6.02 x 1023 particles, atoms, molecules, etc., of a substance in 1 mole of that substance. In other words, each sample would contain 6.02 x 1023 particles per mole, or 6.02 x 1023 particles/mol.
The process of stoichiometry can be used to calculate the mass of a compound either required or produced during a chemical reaction. It can also be used to calculate the number of particles used or produced, or the number of moles used or produced. Mole ratios are used to determine the relationships among moles of various compounds in a reaction, and these ratios can be determined from the coefficients of a balanced chemical equation. The molar masses of reactants and products are used as conversion factors to calculate mass relationships. If the dimensional analysis problems are set up correctly, all of the units should cancel, leaving only the unit of the component that you are looking for.
The following examples show different stoichiometric calculations for the same reaction of the burning of hydrogen gas. The correct and balanced chemical equation for this reaction is:
2 H2 + O2 → 2 H2O
How many moles of water are produced if four moles of hydrogen are burned?
Multiply the numerators, then divide by the denominator(s). Notice how the units cancel, leaving only moles of water. It is important that the mole ratio numbers from the balanced chemical equation are used. Even though it would achieve the same answer, it would be incorrect to change the mole ratios from 2:2 to 1:1.
How many moles of water are produced if four moles of oxygen are consumed?
From this example, it is easy to see why it is critical to understand how to use the mole ratios from the chemical equation. The same number of moles of oxygen and hydrogen do not produce the same amount of water.
Stoichiometry may also be used to convert from moles to grams. In this case, if the amount of a reactant is known, this can be used to calculate the mass of any other component of the chemical equation.
How many grams of water are produced from 3.5 mol H2?
Putting it all together, stoichiometry may be used to find the amount (in grams) used or produced if the amount (in grams) of any other substance in the chemical equation is known.
How many grams of oxygen are required to produce 63 grams of H2O?
You may also use conversion factors to find the number of particles in a sample.
How many molecules of water are in that 63 gram sample?
Calculating the Limiting Reagent
A limiting reagent is the reactant that is completely consumed first and, therefore, determines the amount of product formed in a reaction. When one of the reactants is completely consumed in a chemical reaction, the reaction stops and no further products may be formed. Chemists rarely mix reactants in the exact ratios specified by the balanced equation. Usually, they mix reactants in ratios that allow one reactant to be the limiting reagent. The other reactants are said to be in excess as unreacted portions of these reactants remain as leftovers after the reaction is over. To calculate the limiting reactant, use stoichiometry to determine which reactant is consumed first, then use the amount of this reactant to find the moles or mass of product formed.
The picture below illustrates what occurs during a chemical reaction. In the first container, there are six molecules of hydrogen gas (H2) and four molecules of nitrogen gas (N2). How many molecules of ammonia (NH3) will be produced? The balanced chemical equation is:
N2 + 3 H2 → 2 NH3
Only four molecules of ammonia can be produced. During the chemical reaction, it takes three hydrogen atoms per one nitrogen atom to create an ammonia molecule. In this case, the limiting reagent is hydrogen. Once all of the hydrogen is used, no further product can be formed, and the reaction stops.
Describing Reaction Products
Chemists describe the amount of product formed in a chemical reaction as yield. In chemistry, yield may be used, or described, in three different ways. There is theoretical yield, actual yield, and percent yield:
Theoretical Yield: Theoretical yield is a calculated value. It represents the quantity of product expected based on the quantity of a limiting reagent used in a reaction. This yield assumes that 100% of the limiting reagent is converted to product in an ideal chemical reaction.
Actual Yield: Actual yield is an observed, measured value. It represents the actual quantity of product formed, isolated, and then measured following a chemical reaction. Often, the actual yield is lower than the theoretical yield. For example, a reaction may not proceed with 100% conversion of limiting reagent to products. In addition, some product may not be recovered during the steps following the reaction. Finally, some products are not very stable and may break down after reaction, which may also decrease the final quantity isolated.
Percent Yield: Percent yield is a calculated value that provides an indication of how successfully product was isolated. Percent yield is found by dividing the actual yield by the theoretical yield and then multiplying the result by 100 to express a percentage.
From the analysis of theoretical yield and actual yield, we can study which factors influence the actual amount, and what steps can be taken to make the amount closer to the theoretical yield.