Study Notes for Writing and Balancing Chemical Equations

7.1 Writing and Balancing Chemical Equations
LEARNING OBJECTIVES

  • By the end of this section, you will be able to:

    • Derive chemical equations from narrative descriptions of chemical reactions.

    • Write and balance chemical equations in molecular, total ionic, and net ionic formats.

Introduction to Chemical Equations

  • Chemical equations use element symbols to represent individual atoms.

  • When atoms gain or lose electrons to form ions, or when they combine to create molecules, their symbols are modified or combined to yield chemical formulas.

  • To represent the identities and relative quantities of substances involved in a chemical (or physical) change, one must write and balance a chemical equation.

Example Reaction

  • Consider the reaction of methane (CH4) with oxygen (O2):

    • Reactants: 1 Methane (CH4) and 2 Diatomic Oxygen (O2)

    • Products: 1 Carbon Dioxide (CO2) and 2 Water (H2O)

  • The chemical equation for this process is represented as:
    CH4 + 2O2 \rightarrow CO2 + 2H2O

Fundamental Aspects of Chemical Equations

  1. Reactants: The substances that underwent reaction, displayed on the left side of the equation.

  2. Products: The substances generated from the reaction, displayed on the right side of the equation.

  3. Plus Signs (+): Separate individual reactant and product formulas.

  4. Arrow ($\rightarrow$): Separates the reactant side from the product side of the equation.

  5. Coefficients: Numbers placed immediately to the left of each formula to indicate the relative amounts, often expressed in the smallest whole-number terms.

  • Example Ratio Interpretation:

    • Methane to oxygen to carbon dioxide to water ratio is 1:2:1:2.

    • Valid interpretations include:

    • One methane molecule reacts with two oxygen molecules yielding one carbon dioxide molecule and two water molecules.

    • One mole of methane reacts with two moles of oxygen yielding one mole of carbon dioxide and two moles of water.

Balancing Equations

  • A balanced chemical equation ensures equal numbers of each type of atom on both sides, adhering to the law of conservation of matter. This means:

    • The number of atoms for each element must be equal in both reactants and products.

    • Example calculation for the methane-oxygen reaction:

    • Count atoms:

      • C: 1 (reactant) = 1 (product)

      • H: 4 (reactant) = 4 (product)

      • O: 4 (reactant) = 4 (product)

    • Confirmed balanced since each element maintains equality.

Method: Balancing by Inspection

  • Balancing equations can be achieved through a straightforward method called balancing by inspection.

  • Example for the decomposition of water (H_2O):

    • Unbalanced equation shows H: 2 \neq O: 1.

  • After adjusting coefficients, the balanced equation is:
    2H2O \rightarrow 2H2 + O_2

  • Note: Subscripts in formulas cannot be changed since they define the substance's identity.

Example of Balancing Chemical Equation

  • For the reaction of molecular nitrogen (N2) and oxygen (O2) to form dinitrogen pentoxide (N2O5), begin with:

    • Unbalanced Equation:
      N2 + O2 \rightarrow N2O5

    • Count atoms:

    • N: 2 (reactants) vs. 2 (products), balanced.

    • O: 2 (reactants) vs. 5 (products), not balanced.

  • Changing coefficients brings balance:
    2N2 + 5O2 \rightarrow 2N2O5

Advanced Balancing Techniques

  • Fractional Coefficients: In some cases, employing fractions can simplify the balancing process temporarily.

  • Example: Balancing of ethane (C2H6) with oxygen before converting fractional coefficients to integers by multiplying through:
    C2H6 + \frac{7}{2}O2 \rightarrow 2CO2 + 3H2O Multiplying by 2 yields: 2C2H6 + 7O2 \rightarrow 4CO2 + 6H2O

Information Included in Chemical Equations

  • Physical States: Indicated with abbreviations following formulas:

    • (s): solid

    • (l): liquid

    • (g): gas

    • (aq): aqueous, for substances dissolved in water.

  • Example: The reaction of sodium (Na) in water (H2O) producing hydrogen gas (H2) and sodium hydroxide (NaOH):
    2Na(s) + 2H2O(l) \rightarrow H2(g) + 2NaOH(aq)

Conditions for Reactions

  • Special conditions may be noted above or below the arrow:

    • Heating is indicated by the Greek letter delta (\Delta).

Ionic Reactions

  • Reactions in aqueous solutions often involve ions, which can be represented in varying detail.

  • Example reaction between calcium chloride (CaCl2) and silver nitrate (AgNO3):

    • Molecular Equation:
      CaCl2(aq) + 2AgNO3(aq) \rightarrow Ca(NO3)2(aq) + 2AgCl(s)

    • Complete Ionic Equation: Dissociates all aqueous ionic compounds:
      Ca^{2+}(aq) + 2Cl^{-}(aq) + 2Ag^{+}(aq) + 2NO3^{-}(aq) \rightarrow Ca^{2+}(aq) + 2NO3^{-}(aq) + 2AgCl(s)

Net Ionic Equation

  • Remove spectator ions to yield:
    Ag^{+}(aq) + Cl^{-}(aq) \rightarrow AgCl(s)

  • This represents the actual chemical change taking place.

Additional Example of Ionic Reactions

  • Dissolving Carbon Dioxide: In reaction with sodium hydroxide (NaOH):

    • Molecular equation, complete ionic equation, and net ionic equation can be derived using similar balancing methods as previously discussed.