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PV=nRT, the Ideal Gas Law, what is it and how to use it

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Pressure and volume relationship of a gas

Boyle's law

All the particles (atoms and molecules) of a substance are continually moving and so possess kinetic energy. In gases the movement of the particles is highly energetic and this is the reason why gases form, the particles have enough energy to overcome the attractive forces holding the particles together. In gases the particles are moving very quickly and freely in a random manner constantly bumping into each other and their surroundings. It is these collisions between the particles of the gas and the walls of the container it is confined to that creates gas pressure. The gas pressure is the overall force of all these collisions divided by the area of the walls of the container it is confined in.

The relationship of a gas with pressure and volume was developed by the scientist Robert Boyle at around 1660 and is known as Boyle's Law.
Boyle's law states: "For a fixed mass of gas, at a constant temperature, the product (pressure x volume) is a constant."
The animation below gives and explanation of Boyle's law:

A sealed cylinder with no leaks contains a fixed mass of a gas kept at a constant temperature. The gas pressure is created by the collision of the moving gas particles with each other and against the walls of the cylinder.

The above set up is used to investigate the relationship between pressure and volume for a gas. A force is exerted on the piston to compress the gas. The corresponding pressure and volume values are recorded for different applied forces.

By plotting the recorded values of pressure (p) against volume (V) a curve is produced. We can see from the values that when the pressure is doubled the volume is halved. If the pressure was to increase by 3 the volume would decrease to a third. Thus, the volume is inversely proportional to the pressure. By plotting pressure (p) against the reciprocal of the volume (1/V) a straight line is obtained the gradient of which is the constant in Boyle's Law.

A decrease in volume increases the number of gas particles per unit volume. This results in an increase in the number of gas particles close to the cylinder walls and therefore an increase in the number of collisions with the wall. As the number of collisions per unit area increases so does the force per unit area thereby giving an increase in pressure.

Boyle's Law Example:

Using the example of the sealed cylinder above, the volume of gas at the start is 50 cm ³ with a pressure of 1.2 x 10 ⁵ Pascals. The piston is pushed slowly into the syringe until the pressure on the gauge reads 2.0 x 10 ⁵ Pascals. What is the volume of gas?

Solution:

We know

p x V = constant

therefore,
V₂ = 30 cm³

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Pressure and volume relationship of a gas - Boyle's law - Pass My Exams: Easy exam revision notes for GSCE Physics

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Comprehensive revision notes for GCSE exams for Physics, Chemistry, Biology

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State of matter

The material around us exists in three states (solid, liquid, gas) depending on temperature. Solids do not change shape and volume like ice, trees, and so on. The liquid has the property of flowing like water and juice, and the shape changes according to the vessel, but the volume does not change at a constant temperature and pressure. Gases such as air and carbon dioxide are not uniform in shape and volume, and the volume of the gas varies greatly with temperature and pressure.

When the ice is heated, it becomes water. When the water is heated continuously, it becomes water vapor. Conversely, when water vapor cools, it becomes water, and when water is cooled, it becomes ice. When a substance is heated or cooled, the state of the substance changes, which is called a state change.

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The material around us exists in three states (solid, liquid, gas) depending on temperature. Solids do not change shape and volume like ice, trees, and so on. The liquid has the property of flowing like water and juice, and the shape changes according to the vessel, but the volume does not change at a constant temperature and pressure.

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Pressure and temperature relationship of a gas

The Pressure Law

The pressure law states:
"For a fixed mass of gas, at a constant volume, the pressure (p) is directly proportional to the absolute temperature (T)."
Pressure ∝ Temperature

The animation below gives and explanation of the Pressure law:

A sealed cylinder with no leaks contains a fixed mass. The volume of the gas is kept constant by using a cylinder with a fixed roof capable of withstanding high pressures.The gas pressure is created by the collision of the moving gas particles with each other and against the walls of the cylinder.

The following set up is used to investigate the relationship between temperature and pressure for a gas. Heat energy is applied to the cylinder and the temperature of the gas increases. The average velocity of the gas particles increases resulting in an increase in the rate of collisions and the average force per collision. Because the areas of the walls are kept constant, the force per unit area increases resulting in an increase in pressure.

Plotting the pressure (p) against the absolute temperature (T) gives a straight line which when extrapolated passes through the origin. This shows the pressure of the gas is directly proportional to the absolute temperature of the gas. Doubling the temperature will double the pressure for a fixed mass of gas at constant volume. The gradient of the slope is the constant in Charles' Law. It also shows that if the gas is cooled to absolute zero then the energy of the molecules is at the lowest energy state and therefore cannot generate any pressure.

Pressure Law Example:

Using the example of the sealed cylinder above the pressure of gas is recorded as 1.0 x 10 ⁵ N/m ² at a temperature of 0°C. The cylinder is heated further till the thermometer records 150°C. What is the pressure of the gas?

Solution:

We know

p/T = constant

therefore,

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Pressure and temperature relationship of a gas - The Pressure Law - Pass My Exams: Easy exam revision notes for GSCE Physics

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Comprehensive revision notes for GCSE exams for Physics, Chemistry, Biology

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Charle’s Law Assuming constant pressure, increasing the temperature of the gas will speed up the molecular motion. As the gas often collides with the vessel wall, the volume increases. Conversely, if you lower the temperature of the gas, the molecular…

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0:00 / 0:30•Watch full video

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Boyle's Law (⚡3d animation) , Chemistry , Class 11

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1. Atmospheric pressure is the force per unit area exerted by the air that forms the atmosphere on the earth’s surface. 2. Atmospheric pressure varies with altitude 3. Barometers are instruments used to measure atmospheric pressure.4. The SI unit of pressure is the pascal (Pa).5.  1atm is the standard air pressure measured at the earth’s beach

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1. Atmospheric pressure is the force per unit area exerted by the air that forms the atmosphere on the earth’s surface. 2. Atmospheric pressure varies with altitude 3. Barometers are instruments used to measure atmospheric pressure.4. The SI unit of pressure is the pascal (Pa).5.  1atm is the standard air pressure measured at the earth’s beach

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* You have to wear gloves when handling mercury.

Torricelli's Experiment

The first person to measure the magnitude of air pressure is Italian scientist Torricelli. He was filled with mercury (Hg) in a glass tube with one end blocked. And he stood upside down in a bowl of mercury. Then they found that mercury descended to a height of about 76 cm and stopped.

Even if the glass tube's thickness or slope changes, the mercury column's height does not change. This is because the pressure is equal to the air pressure acting on the mercury's surface and the glass tube's mercury column.

Atmospheric pressure on several planets

1atm is the standard air pressure measured at the earth's beach. As you climb higher from the surface, the atmospheric pressure decreases. In outer space, it is '0'.
The moon is '0'atm because there is no air.
Venus is known to have about 90 times the air pressure on Earth due to the thick atmosphere of carbon dioxide.
Mars has a thin atmospheric layer of carbon dioxide. The average air pressure is about 0.006 atmospheres. In winter, the carbon dioxide freezes, so the air pressure goes down.

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You have to wear gloves when handling mercury. Torricelli's Experiment The first person to measure the magnitude of air pressure is Italian scientist Torricelli. He was filled with mercury (Hg) in a glass tube with one end blocked. And...

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The force applied per unit area is called pressure. If the force applied to any two points is the same, the larger the area, the smaller the pressure. Conversely, the smaller the area, the greater the pressure. This is why it hurts more if pointed shoes step on it compared to sneakers.

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