Theory Exercises

Chemical reactions transform reactants into products.

1. Reactants, products and chemical notation

  • Reactants are written on the left side of the arrow.
  • Products are written on the right side of the arrow.
  • A subscript indicates atoms inside one molecule and must not be changed.
  • A coefficient indicates how many molecules or moles participate.
\[\text{Reactants} \rightarrow \text{Products}\]

Chemical Reactions

2. Fundamental laws of chemistry

Lavoisier's law (conservation of mass)

In a chemical reaction, matter is neither created nor destroyed.

Proust's law (definite proportions)

A pure compound always contains the same elements in a fixed mass ratio.

3. Stoichiometry and balancing equations

Stoichiometry studies quantitative relationships between reactants and products.

  • Balance equations by changing only coefficients.
  • Do not change subscripts.
  • Final coefficients should be the smallest whole numbers.

Mass conservation in a balanced equation:

\[\sum m_{\text{reactants}} = \sum m_{\text{products}}\]

4. Thermochemistry

Thermochemistry studies heat exchange during reactions.

  • Exothermic reactions release heat to the surroundings.
  • Endothermic reactions absorb heat from the surroundings.

Endothermic Exothermic

Using the sign convention for energy change:

\[\begin{aligned} \Delta E < 0 &\quad \text{exothermic} \\ \Delta E > 0 &\quad \text{endothermic} \end{aligned}\]

5. Chemical kinetics (reaction rate)

Reaction rate depends on how often and how effectively particles collide.

Collision theory

For a reaction to occur, particles must collide with:

  • Correct orientation.
  • Enough energy to overcome the activation barrier.

Activation energy

The minimum required energy is the activation energy \(E_a\).

Catalysts and enzymes

  • A catalyst speeds up a reaction by lowering \(E_a\) and is not consumed.
  • Enzymes are biological catalysts.

Factors that usually increase rate: temperature, concentration, pressure (in gases), and contact surface.

Catalysts

6. The mole and Avogadro constant

The mole (mol) is the SI unit for amount of substance.

\[1\,\text{mol} = 6.022 \times 10^{23}\,\text{particles}\]

This value corresponds to the number of atoms in exactly \(12\,\text{g}\) of carbon-12.

Example

For \(2.6\,\text{mol}\) of water:
\(N = nN_A = 2.6 \times 6.022 \times 10^{23} \approx 1.57 \times 10^{24}\,\text{molecules}\)
Hydrogen atoms in that sample:
\(N_{\mathrm{H}} = 2N \approx 3.14 \times 10^{24}\,\text{atoms}\)

7. Molar mass and mass-mole conversion

Molar mass \(M\) (in \(\text{g/mol}\)) connects mass and moles:

\[n = \frac{m}{M}\]
For carbon dioxide:

\(M(\mathrm{CO}_2) = 12 + 2\cdot 16 = 44\,\text{g/mol}\)
If \(m=80\,\text{g}\):
\(n = \frac{80}{44} \approx 1.82\,\text{mol}\)

8. Common reaction types

  • Combustion: hydrocarbon + oxygen \(\rightarrow\) carbon dioxide + water.
  • Acid-base neutralization: acid + base \(\rightarrow\) salt + water.
Examples

Combustion of methane:
\(\mathrm{CH}_4 + 2\mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O}\)
Neutralization of hydrochloric acid with sodium hydroxide:
\(\mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_2\mathrm{O}\)

9. Limiting reactant

In real reactions, reactants are often not in perfect stoichiometric proportion.

  • The limiting reactant is consumed first and determines the maximum product formed.
  • The other reactant is in excess.