The Gas Laws

 

This is part of Year 11 HSC Chemistry course under the topic of Gas Laws.

HSC Chemistry Syllabus

  • Conduct investigations and solve problems to determine the relationship between the Ideal Gas Law and:
    • Gay-Lussac's Law (Temperature)
    • Boyle's Law
    • Charles' Law
    • Avogadro's Law

    The Gas laws

    The gas laws describe the relationships between pressure, volume, and temperature of ideal gases. These laws were developed by four distinguished scientists – Robert Boyle, Jacques Charles, Joseph Louis Gay-Lussac, and Amedeo Avogadro – in the late 18th century. Ideal gases follow these mathematical relationships under perfect circumstances. The gas laws culminated in the Ideal Gas Law, a combined expression representing these relationships. 

     

    Boyle's Law

    Boyle's law states the volume of a given amount of gas is inversely proportional to the applied pressure when temperature and amount are held constant. This means that as the pressure of a gas increases, its volume decreases since the gas particles are forced closer together

    Conversely, when pressure decreases, the volume increases as the particles have more space to move apart. An example of this phenomenon can be seen in weather balloons, which expand as they rise to higher altitudes where pressure is lower.

    The gas laws originate from the ideal gas law `PV = nRT` and Boyle's law describes the following mathematical relationship when temperature and amount are held constant 

     

    $$PV = k \text{  (where } k \text{  is a constant  )}$$

      

    $$P \propto \frac{1}{V}$$

     

    $$P_1V_1 = P_2V_2$$

     

    The relationship between volume and pressure as described by Boyle's Law is demonstrated on the following graph. 

     

     

    Real-World Applications of Boyle's Law:

    • Breathing and lung function – diaphragm moves down to increase volume and decrease pressure in lungs
    • Syringe – pushing plunger decreases volume to increase pressure (like bike pump)
    • Balloon – when balloons are squeezed, volume decreases so pressure inside increases.

     

    Charles's Law: Volume and Temperature

    Charles's Law states that if the volume of a container of gas increases at constant pressure and mass, the temperature must also increase, and vice versa. Hot air balloons rise because gases expand when heated. This is why warm air collects near the ceiling while cooler air settles at ground level. 

     

    $$V = kT \text{  (where } k \text{  is a constant at a given temperature)}$$

     

    $$V \propto T$$

     

    $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

     

     

    Real-World Applications of Charles's Law:

    Hot air balloon – increasing the temperature of air causes it to increase its volume and become less dense than surrounding air

    Bread baking – increasing temperature causes gas to expand in dough.

     

    Gay-Lussac's Law: Pressure and Temperature

    Gay-Lussac’s Law states that the pressure of a gas is directly proportional to its temperature, provided the volume and the amount of gas remain constant. This means that if the temperature of a gaseous system increases, so does the temperature and vice versa. 

    The mathematical representation of this relationship is  

     

    $$\frac{P}{T} = k \text{  (where } k \text{  is a constant at constant temperature and amount)}$$

     

    $$P \propto T$$

     

    $$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

     

    The relationship between pressure and temperature as described by Gay-Lussac's law is demonstrated on the graph below. 

     

     


    Real-World Applications of Gay-Lussac's Law:

    • Pressure cooker – food is sealed in steam which increases the pressure inside the cooker. As the temperature rises so does the pressure
    • Aerosol Cans – have warnings to avoid open fires. Increase in temperature builds pressure in the can which can cause explosions.

     

    Avogadro's Law: Volume and Amount of Gas

    Avogadro's Law states ideal gases containing the same number of molecules occupy an equal volume at the same pressure and temperature.

     

    $$V \propto n \text{ (where } n \text{ is the amount of gas, and pressure } P \text{ and temperature } T \text{ are fixed)}$$

     

    $$V = k \times n \text{  where }k \text{   is a constant at a given temperature}$$

     

     

     

    Real-World Applications of Avogadro's Law:

    • Gas storage requirements – how much gas can be stored in a certain amount of space
    • Determining the stoichiometric amounts in reactions – determining amounts of gas produced via gas syringing.

    BACK TO MODULE 2: INTRODUCTION TO QUANTITATIVE CHEMISTRY