• Gases?in a container exert a?pressure?as the gas molecules are constantly?colliding?with the walls of the container

Gas particles exert a pressure by constantly colliding with the walls of the container

Changing gas volume

• Decreasing?the?volume?(at constant temperature) of the container causes the molecules to be?squashed?together which results in more?frequent?collisions with the container wall
• The?pressure?of the gas?increases

Decreasing the volume of a gas causes an increased collision frequency of the gas particles with the container wall

• The?pressure?is therefore?inversely proportional?to the?volume?(at constant temperature)
• This is known as?Boyle's Law
• Mathematically, we say P ∝ 1/V or?PV = a constant
• We can show a graphical representation of?Boyle's Law?in three different ways:
  • A graph of pressure?of gas plotted against 1/ volume gives a straight line
  • A graph of pressure against volume gives a curve
  • A graph of PV versus P gives a straight line

Three graphs that show Boyle’s Law

Changing gas temperature

• When a gas is?heated?(at constant pressure) the particles gain more?kinetic energy?and undergo more?frequent collisions?with the container walls
• To keep the?pressure constant, the molecules must get further apart and therefore the?volume increases
• The?volume?is therefore?directly proportional?to the?temperature in Kelvin?(at constant pressure)
• This is known as?Charles' Law
• Mathematically, V ∝ T or?V/T = a constant
• A graph of?volume?against?temperature in Kelvin?gives a straight line

Increasing the temperature of a gas causes an increased collision frequency of the gas particles with the container wall (a); volume is directly proportional to the temperature in Kelvin (b)

Changing gas pressure

• Increasing?the?temperature?(at constant volume) of the gas causes the molecules to gain more?kinetic energy
• This means that the particles will move?faster?and?collide?with the container walls more?frequently
• The?pressure?of the gas?increases
• The?temperature?is therefore?directly proportional?to the?pressure?(at constant volume)
• Mathematically, we say that P ∝ T or?P/T = a constant?
• A graph of?temperature in Kelvin?of a gas plotted against?pressure?gives a straight line

Increasing the temperature of a gas causes an increased collision frequency of the gas particles with the container wall (a); temperature is directly proportional to the pressure (b)

Pressure, volume and temperature

• Combining these three relationships together:
  • P/V = a constant
  • V/T = a constant
  • P/T = a constant
• We can see how the?ideal gas equation?is constructed
  • PV/T = a constant
  • PV = a constant x T
• This constant is made from two components, the number of?moles,?n, and the?gas constant,?R, resulting in the overall equation:
  • PV = nRT

Changing the conditions of a fixed amount of gas

• For a fixed amount of gas,?n?and?R?will be constant, so if you change the conditions of a gas we can ignore?n?and?R?in the?ideal gas equation
• This leads to a very useful expression for problem solving
• Where P₁, V_1?and T_1?are the initial conditions of the gas and P₂, V_2?and T_2?are the final conditions

Answer:

Step 1: Rearrange the formula to change the conditions of a fixed amount of gas. Pressure is constant so it is left out of the formula

Step 2: Convert the temperature to Kelvin. There is no need to convert the volume to m^3??because the formula is using a?ratio?of the two volumes

V_1?= 20 dm^3?

V_2?= 10 dm^3?

T_1?= 25 + 273 = 298 K

Step 3: Calculate the new temperature

Answer:

Step 1: Rearrange the formula to change the conditions of a fixed amount of gas

Step 2: Substitute in the values and calculate the final pressure

P_1?= 80 kPa

V_1?= 2.00 dm^3?

V_2?= 2.25 dm^3?

T_1?= 20 + 273 = 293 K

T_2?= 70 + 273 = 343 K