Essential Concepts and Calculations in Chemistry

Posted on Nov 15, 2025 in Chemistry

Properties of Water

  • Polarity: Water molecules are polar, meaning they have a slight positive charge on the hydrogen atoms and a slight negative charge on the oxygen atom.
  • Hydrogen Bonding: The polarity of water molecules allows them to form strong hydrogen bonds with each other.
  • Cohesion and Adhesion: Water molecules are attracted to each other (cohesion) and to other polar surfaces (adhesion).
  • High Heat Capacity: Water can absorb a large amount of heat energy without a significant change in temperature.
  • High Heat of Vaporization: A large amount of energy is needed to convert liquid water into steam.
  • Excellent Solvent: Water can dissolve many different substances, making it an important solvent in biological and chemical processes.
  • Density Anomalies: Water is denser as a liquid than as a solid, which is why ice floats on water.

Temperature and Average Kinetic Energy

  • Direct Proportionality: Temperature and the average kinetic energy of particles are directly proportional. As temperature increases, the average kinetic energy of the particles increases, and vice versa.
  • Increased Molecular Motion: Higher temperatures mean that molecules are moving faster and more vigorously.
  • Kinetic Energy: Kinetic energy is the energy associated with the motion of molecules.

Characteristics of Dynamic Equilibrium

  • Reversible Reactions: Dynamic equilibrium occurs in reversible reactions where both the forward and reverse reactions are happening simultaneously.
  • Equal Rates: The rate of the forward reaction (reactants to products) is equal to the rate of the reverse reaction (products to reactants).
  • Constant Concentrations: While the reactions are still occurring, the concentrations of reactants and products remain constant because the rates are equal.
  • Closed System: Dynamic equilibrium typically occurs in closed systems where no reactants or products can be added or removed.
  • Constant Motion: Molecules in a dynamic equilibrium are constantly in motion, engaging in both forward and reverse reactions.

Determining Limiting and Excess Reactants

To determine the limiting reactant and excess reactants, calculate the theoretical yield of the product based on each reactant. The reactant that produces the smallest amount of product is the limiting reactant, while the other is in excess.

Example Calculation: Hydrogen and Oxygen

Given: 4.0 grams of H₂ and 8.0 grams of O₂

Reaction: 2H₂(g) + O₂(g) → 2H₂O(g)

  1. Balanced Equation: The equation is already balanced.
  2. Convert to Moles:
    • Molar mass of H₂: 2.02 g/mol
    • Moles of H₂: 4.0 g / 2.02 g/mol ≈ 1.98 moles
    • Molar mass of O₂: 32.00 g/mol
    • Moles of O₂: 8.0 g / 32.00 g/mol = 0.25 moles
  3. Calculate Moles of Product (H₂O):
    • Moles of H₂O from H₂: 1.98 moles H₂ × (2 moles H₂O / 2 moles H₂) = 1.98 moles H₂O
    • Moles of H₂O from O₂: 0.25 moles O₂ × (2 moles H₂O / 1 mole O₂) = 0.50 moles H₂O
  4. Determine Limiting and Excess Reactants:
    • Since O₂ produces fewer moles of H₂O (0.50 moles), it is the limiting reactant.
    • H₂ is the excess reactant.

The Ideal Gas Law (PV=nRT)

The Ideal Gas Law, PV = nRT, can be used to calculate the values of pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas when three of these variables are known.

R (Ideal Gas Constant) = 0.0821 L·atm/mol·K

Calculating Variables using PV=nRT

Here is how to use the equation to calculate each variable:

  1. Calculating Pressure (P):
    • Equation: P = nRT/V
    • Steps: Identify n, R, T, and V. Substitute the values and solve for P. Ensure units are consistent (e.g., P in atm, V in liters, T in Kelvin).
  2. Calculating Volume (V):
    • Equation: V = nRT/P
    • Steps: Identify n, R, T, and P. Substitute the values and solve for V. Ensure units are consistent.
  3. Calculating Number of Moles (n):
    • Equation: n = PV/RT
    • Steps: Identify P, V, R, and T. Substitute the values and solve for n. Ensure units are consistent.
  4. Calculating Temperature (T):
    • Equation: T = PV/nR
    • Steps: Identify P, V, n, and R. Substitute the values and solve for T. Ensure units are consistent.

Ideal Gas Law Example Calculation

Let’s calculate the temperature (T) for 0.5 moles of a gas at a pressure of 2 atm and a volume of 10 L. (R = 0.0821 L·atm/mol·K)

Equation: T = PV/nR

Substitute: T = (2 atm)(10 L) / (0.5 mol)(0.0821 L·atm/mol·K)

Solve: T = 20 / 0.04105 ≈ 487.2 K

Heat Equations: Calculating Heat Transfer (Q = mcΔT)

  1. Identify the Variables:
    • Q or q: Represents the heat energy transferred in joules (J).
    • m: Represents the mass of the substance in grams (g) or kilograms (kg).
    • c: Represents the specific heat capacity of the substance (J/g·°C or J/kg·K). This is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius (or Kelvin).
    • ΔT: Represents the change in temperature, calculated as the final temperature minus the initial temperature (Tf – Ti).
  2. Calculate the Temperature Change (ΔT):
    • ΔT = Tf – Ti
  3. Substitute the Values into the Equation:
    • Q = mcΔT
  4. Solve for Q:
    • Multiply the mass (m), specific heat capacity (c), and temperature change (ΔT) to find the heat energy (Q).

Heat Equation Example

Calculate the heat required to raise the temperature of 50 grams of water from 20°C to 80°C. (Specific heat capacity of water = 4.184 J/g·°C).

Identify the variables:

  • m = 50 g
  • c = 4.184 J/g·°C
  • ΔT = 80°C – 20°C = 60°C

Substitute the values:

Q = (50 g) × (4.184 J/g·°C) × (60°C)

Solve for Q:

Q = 12,552 J

Therefore, 12,552 joules of heat are required.

Calculating Reaction Yield

To calculate percent yield, divide the actual yield by the theoretical yield and multiply by 100.

Formulas:

  • Percent Yield: (Actual Yield / Theoretical Yield) × 100
  • Actual Yield: (Percent Yield / 100) × Theoretical Yield

Endothermic and Exothermic Reactions

  • Endothermic Reactions: Absorb heat from their surroundings (ΔH > 0).
  • Exothermic Reactions: Release heat into their surroundings (ΔH < 0).

Enthalpy (H) is a measure of the total energy of a system, and ΔH represents the change in enthalpy during a reaction. The activation energy (Ea) is the minimum energy required for a reaction to occur.

Properties of States of Matter

Solids

  • Shape and Volume: Solids have a fixed shape and a fixed volume.
  • Arrangement of Particles: Particles are tightly packed and arranged in a regular pattern.
  • Movement of Particles: Particles primarily vibrate in place, with little movement.
  • Example: A chair, a book, or a piece of wood.

Liquids

  • Shape and Volume: Liquids have a definite volume but take the shape of their container.
  • Arrangement of Particles: Particles are close together but not in a regular arrangement.
  • Movement of Particles: Particles move around and slide past each other.
  • Example: Water, milk, or juice.

Gases

  • Shape and Volume: Gases have neither a fixed shape nor a fixed volume.
  • Arrangement of Particles: Particles are widely separated and have no regular arrangement.
  • Movement of Particles: Particles move freely and rapidly in all directions.
  • Example: Air, water vapor, or oxygen.

Stoichiometry: Calculating Reaction Quantities

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in chemical reactions.

  1. Balanced Chemical Equation: A balanced chemical equation provides the molar ratios between reactants and products. It ensures that the number of atoms of each element is equal on both sides, according to the law of conservation of mass.
  2. Converting to Moles: Convert the given quantities (e.g., grams, liters) to moles using appropriate conversion factors (like molar mass for solids or the ideal gas law for gases).
  3. Using Mole Ratios: Use the coefficients from the balanced equation to determine the moles of another substance involved in the reaction.
  4. Converting to Desired Units: Convert moles of the desired substance back to the required units (e.g., grams, liters) using the appropriate conversion factors.

Stoichiometry Example

Calculate the grams of product B produced from 10 grams of reactant A.

  1. Balanced Equation: Assume the balanced equation is: 2A + 3B → 4C.
  2. Convert A to Moles: If the molar mass of A is 20 g/mol, then 10 g of A is 10 g / 20 g/mol = 0.5 moles of A.
  3. Use Mole Ratio: From the balanced equation, 2 moles of A produce 3 moles of B. Therefore, 0.5 moles of A will produce (3/2) × 0.5 = 0.75 moles of B.
  4. Convert B to Grams: If the molar mass of B is 40 g/mol, then 0.75 moles of B is 0.75 mol × 40 g/mol = 30 grams of B.

Phase Changes

Phase Change as a Physical Change

Phase changes are physical processes, meaning they alter the state of a substance without changing its chemical composition.

Types of Phase Changes

  • Melting: Solid to liquid.
  • Freezing: Liquid to solid.
  • Vaporization: Liquid to gas.
  • Condensation: Gas to liquid.
  • Sublimation: Solid directly to gas.
  • Deposition: Gas directly to solid.

Understanding pH

pH is a measure of the relative amount of free hydrogen (H⁺) and hydroxyl (OH⁻) ions in the water.

  • pH less than 7 indicates acidity.
  • pH greater than 7 indicates a base (alkalinity).
  • pH equal to 7 indicates neutrality.

Mole Ratios in Chemical Reactions

The mole ratio is a key concept in stoichiometry, used to relate the amounts of reactants and products.

  • Balanced Equation: A balanced chemical equation shows the quantitative relationship between reactants and products.
  • Coefficients: The numbers in front of each chemical formula represent the number of moles of that substance involved in the reaction.
  • Mole Ratio Calculation: The mole ratio is determined by comparing the coefficients of any two substances in the balanced equation.

Mole Ratio Example

In the reaction 2H₂ + O₂ → 2H₂O:

  • The mole ratio between hydrogen (H₂) and oxygen (O₂) is 2:1.
  • The mole ratio between water (H₂O) and oxygen (O₂) is 2:1.

Applications

Mole ratios are used to solve stoichiometry problems, such as calculating the amount of product formed or the amount of reactant needed.

Catalysts and Reaction Rates

  • Definition: A catalyst is a substance that alters the rate of a chemical reaction without being permanently changed itself.
  • Function: Catalysts work by lowering the activation energy (Ea), which is the minimum energy required for a reaction to occur.

Types of Catalysts

  • Homogeneous catalysts: These are in the same phase as the reactants (e.g., dissolved in the same liquid).
  • Heterogeneous catalysts: These are in a different phase than the reactants (e.g., a solid catalyst interacting with a liquid or gas).

Examples

  • Enzymes: Biological catalysts that speed up biochemical reactions.
  • Acids and bases: Can act as catalysts in various reactions.
  • Metal catalysts: Used in industrial processes (e.g., the Haber-Bosch process).
  • Catalytic converters: Used in automobiles to convert harmful pollutants into less harmful substances.

Molarity and Concentration Calculations

  1. Calculating Molarity:

    Molarity (M) = moles of solute / liters of solution

    Example: If you have 2 moles of solute dissolved in 1 liter of solution, the molarity is 2 M (2 moles/liter).

  2. Mass to Moles Conversion:

    Moles = mass of solute / molar mass of solute

    The molar mass can be found on the periodic table by adding the atomic masses of all the elements in the compound.

    Example: If you have 12.0 g of carbon (C) (molar mass 12.01 g/mol), you have 1.00 mol of carbon (12.0 g / 12.01 g/mol ≈ 1.00 mol).

  3. Moles to Mass Conversion:

    Mass of solute = moles of solute × molar mass of solute

    Example: If you have 0.5 moles of water (H₂O) (molar mass 18.02 g/mol), you have 9.01 g of water (0.5 mol × 18.02 g/mol = 9.01 g).

Using Avogadro’s Number

Avogadro’s number (6.022 × 10²³) represents the number of particles (atoms, molecules, etc.) in one mole of a substance.

  1. Convert from Particles to Moles:

    Divide the number of particles by Avogadro’s number.

  2. Convert from Moles to Mass:

    Multiply the number of moles by the molar mass (g/mol).

Calculating pH and pOH

  1. Calculating pH:

    pH = -log[H₃O⁺]

    Where [H₃O⁺] is the hydronium ion concentration in moles per liter (M).

  2. Calculating pOH:

    pOH = -log[OH⁻]

    Where [OH⁻] is the hydroxide ion concentration in moles per liter (M).

  3. Relationship between pH and pOH:

    pH + pOH = 14 (at 25°C)

    This relationship allows you to calculate one value if you know the other.

Reversible Reactions and Equilibrium

Reversible reactions are reactions where products can transform back into reactants. They are represented by a double arrow (⇌) in chemical equations.

A reversible reaction reaches equilibrium when the rates of the forward and reverse reactions are equal. At this point, the concentrations of reactants and products remain constant, even though the reactions are still occurring.