Chapter 6

Quantities in Chemical Reactions

Shaun Williams, PhD

The Meaning of a Balanced Equation

What do the coefficients in a balanced chemical equation mean?

• Let's consider the combustion of propane: \[ \chem{C_3H_8(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)} \]

The Meaning of the Coefficients

Mole-to-Mole Conversions

• In mole-mole conversions, we relate the moles of a reactant or product to other reactants or products using a mole ratio.
• Mole ratios:
  • are obtained from the coefficients in the balanced chemical equation.
  • help us determine the moles of one substance in a reaction when the number of moles of another substance in the same reaction is known.
  • are used as conversion factors in dimensional analysis problems.

Mass-to-Mass Conversions

• Typically, chemical measuring devices do NOT measure in moles.
• We are often given grams as our beginning unit in problems that use a mole ratio.
• Therefore, we need to convert from grams to moles 1^st.
• The conversion factor we need to convert from grams to moles (or vice versa) is the molar mass (MM).

The Law of Conservation of Mass

• The Law of Conservation of Mass states that the masses of the reactants must equal the masses of the products. \[ \text{Mass Reactants} = \text{Mass Products} \]

Limiting Reactants

What are limiting reactants?

• Take the equation: \[ \chem{2 Na(s) + Cl_2(g) \rightarrow 2 NaCl(s)} \]
• When reactants are not mixed in relative amounts as described by the balanced chemical equation, one reactant does not react completely.
  • In this case, the two reactants are known as:
    • Limiting reactant
      • Reacts completely
      • Limits the amount of the other reactant that can react
      • Limits the amount of product that can be made
    • Excess reactant
      • DOES NOT react completely

Steps for Determining the Limiting Reactant

1. Calculate the amount of one reactant (B) needed to react with the other reactant (A).
2. Compare the calculated amount of B (amount needed) to the actual amount of B that is given.
   1. If calculated B = actual B, there is no limiting reactant. Both A and B will react completely.
   2. If calculated B > actual B, B is the limiting reactant. Only B will react completely.
   3. If calculated B < actual B, A is the limiting reactant. Only A will react completely.

Percent Yield

What is a percent yield?

• Percent yield
  • Describes how much of a product is actually formed in comparison to how much should have been formed
• Theoretical yield
  • The maximum amount of product that can be obtained from given amounts of reactants
• Actual yield
  • The amount of product we measure in the laboratory
  • Usually less than the theoretical yield

\[ \text{% yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\% \]

Energy Changes

The Law of Conservation of Energy

• Energy can be converted or transferred, but it cannot be created or destroyed.
• Heat is energy that is transferred between two objects because of a difference in their temperatures.

Exothermic and Endothermic Reactions

• Exothermic reaction
  • A reaction that releases energy into the surroundings
• Endothermic reaction
  • A reaction that absorbs energy from its surroundings

Specific Heat

• The amount of heat that must be added to \( \chem{1\, g} \) of a substance to raise its temperature by \( 1^\circ C\).
• Units are Joules per gram per degree Celsius [\( \bfrac{\text{J}}{\chem{g\,{}^\circ C}} \)]
• Is specific to the substance. See Table 6.2 for some common specific heats. \[ q = mC \Delta T \] where \(q\) is heat, \(m\) is mass, \(C\) is specific heat, and \(\Delta T\) is the change in temperature

Energy of the System and the Surroundings

\[ \chem{q_{system} + q_{surroundings} =0} \]

• A system can be an object such as a piece of pipe, or a process, such as a physical or chemical change.
• The surroundings are everything around the system.

Heat Changes in Chemical Reactions

How we measure heat

• A bomb calorimeter is used to measure the heat transfer in a chemical reaction.
• Therefore, \[ \chem{q_{reaction} + q_{water} = 0} \] \[ \chem{q_{reaction} + q_{calorimeter} = 0} \]