Reactions and Stoichiometry

Significant Figures in Calculations

Significant figures ("sig figs") are used in chemistry to indicate the precision of measured quantities and to ensure that calculations do not imply greater accuracy than the data support.

• Tracking Significant Figures: Keep track of the number of significant figures in each number throughout a calculation.

• Calculation Process: Perform all calculations with as many digits as possible. Only round the final answer to the correct number of significant figures at the end.

• Purpose: Significant figures indicate how many digits in a number are trustworthy, while rounding is done to avoid reporting digits that are not reliable.

• Tip: Instead of rounding at each step, underline the last significant figure in each intermediate result to keep track.

Example Calculation:

• Final answer rounded to correct sig figs: 3.73

Chemical Reactions

Chemical reactions describe the transformation of substances (reactants) into new substances (products). The process is represented by a chemical equation.

• General Form: Reactants Products

• Example:

• Conservation Laws:

  • The number of atoms of each element must be the same on both sides of the equation.

  • The total charge must be the same on both sides.

Balancing Chemical Reactions

Balancing chemical equations ensures that the law of conservation of mass and charge is obeyed. This is done by adjusting the coefficients of reactants and products.

Simple Balancing Strategy

• Identify a reactant and product containing the same element.

• Adjust coefficients to balance that element.

• Repeat for other elements, leaving hydrogen and oxygen for last if they appear in multiple compounds.

• Adjust all coefficients to the smallest whole numbers possible.

Example:

• Unbalanced:

• Step 1: Balance N:

• Step 2: Balance H:

• Step 3: Balance O:

• Step 4: Make whole numbers:

Algebraic Balancing Strategy

• Assign variables to each coefficient in the equation.

• Write a system of equations for each element.

• Set one coefficient to a constant (e.g., 1) and solve for the others.

Example:

• General:

• Equations:

  • N:

  • H:

  • O:

• Set and solve: , , , $d = 1$

• Multiply to clear fractions:

Formula Weight and Percent Composition

The formula weight (or molecular weight) is the sum of the atomic masses of all atoms in a chemical formula, expressed in atomic mass units (amu). It is used to convert between mass and number of molecules.

• Definition: Formula weight is the mass of one formula unit (or molecule) in amu.

• Definition of amu: the mass of a carbon-12 atom.

• Percent Composition: The percent by mass of an element in a compound is calculated as:

Example:

• Formula weight of :

• Percent mass of Fe:

The Mole and Avogadro's Number

The mole is a counting unit that relates the atomic scale to the macroscopic scale. It is defined as the amount of substance containing as many entities (atoms, molecules, etc.) as there are atoms in exactly 12 grams of carbon-12.

• Definition: items (Avogadro's number).

• Special Property: $1 gram.

• Scale: A mole is an extremely large number; for example, a mole of eggs would weigh about half as much as the moon.

Stoichiometry: Mass-to-Mass Calculations

Stoichiometry involves using balanced chemical equations to calculate the amounts of reactants and products involved in a chemical reaction.

• General Steps:

  1. Convert the mass of a substance to moles using its molecular weight.

  2. Use the mole ratio from the balanced equation to find moles of another substance.

  3. Convert moles back to mass if required.

Example:

• Reaction:

• Given: of

• Find: Mass of needed for complete reaction.

• Molecular weights:

  • :

  • :

• Calculation:

Summary Table: Key Stoichiometric Relationships