# 4: Chemical Calculations

• 4.1: Formulas and Composition
When a reaction is carried out for the first time, little is known about the microscopic nature of the products. It is therefore necessary to determine experimentally the composition and formula of a newly synthesized substance. One way to approach this involves quantitative analysis—the determination of the percentage by mass of each element in the compound. Such data are usually reported as the percent composition.
• 4.2: Writing and Balancing Chemical Equations
Chemical equations are symbolic representations of chemical and physical changes. Formulas for the substances undergoing the change (reactants) and substances generated by the change (products) are separated by an arrow and preceded by integer coefficients indicating their relative numbers. Balanced equations are those whose coefficients result in equal numbers of atoms for each element in the reactants and products.
• 4.3: Reaction Stoichiometry
A balanced chemical equation may be used to describe a reaction’s stoichiometry (the relationships between amounts of reactants and products). Coefficients from the equation are used to derive stoichiometric factors that subsequently may be used for computations relating reactant and product masses, molar amounts, and other quantitative properties.
• 4.4: Reaction Yields
When reactions are carried out using less-than-stoichiometric quantities of reactants, the amount of product generated will be determined by the limiting reactant. The amount of product generated by a chemical reaction is its actual yield, which is often less than the amount of product predicted by the stoichiometry of the balanced chemical equation representing the reaction (theoretical yield). The extent to which a reaction generates the theoretical amount is expressed as its percent yield.
• 4.5: Solution Concentration: Mass Percent
To define a solution precisely, we need to state its concentration: how much solute is dissolved in a certain amount of solvent. Words such as dilute or concentrated are used to describe solutions that have a little or a lot of dissolved solute, respectively, but these are relative terms whose meanings depend on various factors. The mass/mass percent (% m/m) is defined as the mass of a solute divided by the mass of a solution times 100:
• 4.6: Concentration of Solutions
Solution concentrations are typically expressed as molarities and can be prepared by dissolving a known mass of solute in a solvent or diluting a stock solution. The concentration of a substance is the quantity of solute present in a given quantity of solution. Concentrations are usually expressed in terms of molarity, defined as the number of moles of solute in 1 L of solution.
• 4.7: Overview of Spectroscopy
The focus of this chapter is on the interaction of ultraviolet, visible, and infrared radiation with matter. Because these techniques use optical materials to disperse and focus the radiation, they often are identified as optical spectroscopies. For convenience we will use the simpler term spectroscopy in place of optical spectroscopy; however, you should understand that we are considering only a limited part of a much broader area of analytical techniques.
• 4.8: UV