Stoichiometry, Chemical Equations, and Gas Laws: General Chemistry I Study Guide

Stoichiometry and Chemical Equations

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is obeyed. Each side of the equation must have the same number of atoms of each element.

• Step 1: Write the unbalanced equation with correct chemical formulas.

• Step 2: Count the number of atoms of each element on both sides.

• Step 3: Add coefficients to balance the atoms, starting with the most complex molecule.

• Step 4: Check your work to ensure all elements are balanced.

Example: Balance the equation: $\_\_\_\ NH_3 + \_\_\_\ O_2 \rightarrow \_\_\_\ NO + \_\_\_\ H_2O$ Balanced: $4NH_3 + 5O_2 \rightarrow 4NO + 6H_2O$

Types of Chemical Reactions

Chemical reactions can be classified into several types based on the rearrangement of atoms and ions:

• Synthesis (S): Two or more substances combine to form one product. Example: $2H_2 + O_2 \rightarrow 2H_2O$

• Decomposition (D): A single compound breaks down into two or more simpler substances. Example: $2KClO_3 \rightarrow 2KCl + 3O_2$

• Single Replacement (SR): One element replaces another in a compound. Example: $Zn + 2HCl \rightarrow ZnCl_2 + H_2$

• Double Replacement (DR): Exchange of ions between two compounds. Example: $AgNO_3 + NaCl \rightarrow AgCl + NaNO_3$

• Combustion (C): A substance reacts with oxygen, releasing energy, usually as heat and light. Example: $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$

Writing Molecular, Complete Ionic, and Net Ionic Equations

In aqueous reactions, it is important to distinguish between the molecular, complete ionic, and net ionic equations:

• Molecular Equation: Shows all reactants and products as compounds.

• Complete Ionic Equation: Shows all strong electrolytes as ions.

• Net Ionic Equation: Shows only the species that actually change during the reaction.

Example: Potassium chromate and calcium chloride Molecular: $K_2CrO_4(aq) + CaCl_2(aq) \rightarrow CaCrO_4(s) + 2KCl(aq)$ Complete Ionic: $2K^+(aq) + CrO_4^{2-}(aq) + Ca^{2+}(aq) + 2Cl^-(aq) \rightarrow CaCrO_4(s) + 2K^+(aq) + 2Cl^-(aq)$ Net Ionic: $Ca^{2+}(aq) + CrO_4^{2-}(aq) \rightarrow CaCrO_4(s)$

Stoichiometry Calculations

Mole-to-Mole and Mass-to-Mass Conversions

Stoichiometry involves using balanced chemical equations to calculate the relationships between reactants and products in a chemical reaction.

• Mole Ratio: Derived from the coefficients of a balanced equation.

• Mass-to-Mass: Convert mass to moles, use mole ratio, then convert back to mass.

Example: How many grams of $NO$ are produced when 68.4 g of $O_2$ reacts with ammonia at STP? 1. Convert grams $O_2$ to moles: $n = \frac{68.4\ g}{32.00\ g/mol} = 2.14\ mol$ 2. Use mole ratio from balanced equation: $5O_2 : 4NO$ 3. Calculate moles $NO$: $2.14\ mol\ O_2 \times \frac{4\ mol\ NO}{5\ mol\ O_2} = 1.71\ mol\ NO$ 4. Convert moles $NO$ to grams: $1.71\ mol \times 30.01\ g/mol = 51.3\ g$

Gas Laws and Calculations

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and number of moles of a gas:

$PV = nRT$

• P: Pressure (atm)

• V: Volume (L)

• n: Moles of gas

• R: Ideal gas constant ($0.0821\ L\ atm\ mol^{-1}\ K^{-1}$)

• T: Temperature (K)

Example: A balloon contains 30.1 L of $CO_2$ at 47°C and 73 kPa. How many moles of gas does the balloon contain? 1. Convert temperature to Kelvin: $T = 47 + 273 = 320\ K$ 2. Convert pressure to atm: $P = 73\ kPa \times \frac{1\ atm}{101.3\ kPa} = 0.721\ atm$ 3. Solve for n: $n = \frac{PV}{RT} = \frac{0.721 \times 30.1}{0.0821 \times 320} = 0.85\ mol$

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is the sum of the partial pressures of each gas:

$P_{total} = P_1 + P_2 + ... + P_n$

Partial pressure of a gas can be found using mole fraction:

$P_A = X_A \times P_{total}$ $X_A = \frac{n_A}{n_{total}}$

Solution Concentrations and Dilutions

Molarity (M)

Molarity is a measure of concentration, defined as moles of solute per liter of solution:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Example: What is the concentration of a phosphoric acid solution if 97 mL is neutralized by 95 mL of 2.4 M $KOH$?

• Write the balanced equation: $KOH + H_3PO_4 \rightarrow K_3PO_4 + H_2O$

• Use stoichiometry to solve for unknown molarity.

Summary Table: Types of Chemical Reactions

Type	General Form	Example
Synthesis (S)	$A + B \rightarrow AB$	$2H_2 + O_2 \rightarrow 2H_2O$
Decomposition (D)	$AB \rightarrow A + B$	$2KClO_3 \rightarrow 2KCl + 3O_2$
Single Replacement (SR)	$A + BC \rightarrow AC + B$	$Zn + 2HCl \rightarrow ZnCl_2 + H_2$
Double Replacement (DR)	$AB + CD \rightarrow AD + CB$	$AgNO_3 + NaCl \rightarrow AgCl + NaNO_3$
Combustion (C)	$CxHy + O_2 \rightarrow CO_2 + H_2O$	$CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$

Key Takeaways

• Always balance chemical equations before performing stoichiometric calculations.

• Identify the type of reaction to predict products and write net ionic equations.

• Use the ideal gas law and Dalton's law for gas stoichiometry problems.

• Calculate solution concentrations using molarity and dilution equations.

Additional info: These study notes expand on the exam study guide by providing definitions, examples, and step-by-step procedures for balancing equations, classifying reactions, and performing stoichiometric and gas law calculations, as required for General Chemistry I.