Kinetic Theory of Gases
Constant, Random Motion: Gas molecules are always moving in every direction at high speeds. They travel in straight lines until they bump into other gas molecules or hit the walls of the container. This motion is random, meaning the molecules do not follow any pattern and change direction each time they collide.
Elastic Collisions: When gas molecules collide with each other or with the container walls, no energy is lost in the collision. Instead, the energy is transferred or shared between molecules. These collisions are called elastic because the total kinetic energy of all the molecules remains the same, even if individual molecules gain or lose energy.
Pressure Creation: Gas pressure is caused by billions of tiny gas molecules hitting the walls of the container. Each time a molecule hits the wall, it pushes on it with a small force. When all these forces from many collisions are added up over the area of the wall, they create what we call gas pressure.
Negligible Intermolecular Forces: At high temperatures and low pressures, the gas molecules move very quickly and stay far apart from each other. Because they are so far apart, the attraction or repulsion between them is so small that it can be ignored when studying their behavior.
Negligible Volume of Particles: Each gas molecule is extremely tiny compared to the total space inside the container. Because of this, the actual size or volume of the gas particles themselves is considered so small that it doesn’t affect calculations and is usually left out.
Kinetic Energy and Temperature: The average kinetic energy (energy of movement) of the gas molecules increases when the temperature rises. This means that temperature and molecular speed are closely related. When the temperature goes up, molecules move faster and hit the walls more forcefully and more often.
Key Variables in Gas Laws
Pressure (P): Pressure is the amount of force that gas particles apply on the walls of a container per unit area. It depends on how often and how hard the particles hit the walls. We measure pressure in units called Pascals (Pa) or kilopascals (kPa).
Volume (V): Volume is the amount of space that the gas takes up. It can be the size of the container or the balloon that holds the gas. Volume is measured in cubic meters (m³) for large spaces or cubic centimeters (cm³) for smaller spaces.
Temperature (T): Temperature is a measure of how hot or cold the gas is, but for gas laws, it also tells us how fast the gas molecules are moving. Faster molecules mean a higher temperature. In gas law calculations, we must always use the Kelvin scale because it starts from absolute zero.
Boyle’s Law
Pressure-Volume Relationship: Boyle’s Law says that if the temperature stays the same, when the volume of a gas goes down, the pressure goes up. This is an inverse relationship. When gas has less room to move, the molecules hit the walls more often, increasing the pressure.
Mathematical Form: This relationship is written as PV = k, where k is a constant. Another form is P₁V₁ = P₂V₂, which lets us calculate the new pressure or volume if one of them changes.
Explanation: When you compress a gas into a smaller space, the gas molecules have less room to move. They hit the walls of the container more often, which causes the pressure to rise.
Graphical View: If you draw a graph of pressure (P) against volume (V), you will get a curved line going downward. But if you plot pressure against the inverse of volume (1/V), you will get a straight line, showing the inverse relationship.
Charles’s Law
Volume-Temperature Relationship: Charles’s Law tells us that when pressure is kept the same, increasing the temperature will cause the gas to expand, so the volume increases too. This means that volume and temperature are directly proportional.
Mathematical Form: The formula is V/T = k, or V₁/T₁ = V₂/T₂. The temperatures must be in Kelvin because Kelvin starts at absolute zero, which makes the calculations accurate.
Explanation: When gas is heated, the molecules gain energy and move faster. Because they move faster, they push outward more, and the gas takes up more space, increasing the volume.
Graphical View: If you plot the volume of a gas against its temperature in Kelvin, the result will be a straight line going upward. This shows that as temperature increases, volume also increases.
Gay-Lussac’s Law
Pressure-Temperature Relationship: Gay-Lussac’s Law says that if the volume is kept the same, increasing the temperature of a gas will increase its pressure. This is because temperature and pressure are directly related.
Mathematical Form: The formula is P/T = k, or P₁/T₁ = P₂/T₂. Again, temperature must be in Kelvin for the equation to work correctly.
Explanation: When you heat the gas, the molecules move faster and collide with the container walls more frequently and with greater force. This increases the pressure inside the container.
Graphical View: When you plot pressure against temperature in Kelvin, the graph is a straight line going upward, showing the direct relationship between the two.
Absolute Zero and the Kelvin Scale
Definition of Absolute Zero: Absolute zero is the coldest possible temperature. It is the point where gas molecules have no movement at all. This temperature is 0 Kelvin, which equals -273°C.
Theoretical Nature: Scientists cannot actually reach absolute zero in a lab, but they can get very close. It is a helpful idea because it shows the lowest limit of temperature and energy.
Kelvin for Calculations: All gas law calculations must use the Kelvin scale because it starts at absolute zero, which makes the math work correctly and avoids negative temperatures.
Celsius to Kelvin Conversion: To change a temperature from Celsius to Kelvin, just add 273. For example, 25°C is equal to 298 K.
Combined Gas Law
Combined Relationship: The combined gas law puts Boyle’s, Charles’s, and Gay-Lussac’s laws together into one formula. It’s used when pressure, volume, and temperature all change in one situation.
Formula Used: The combined gas law formula is P₁V₁/T₁ = P₂V₂/T₂. You can use this to find out what happens to one variable if the others change, as long as the amount of gas stays the same.
Applications of Gas Laws
Balloons Expanding with Heat: When you warm up a balloon, the air inside heats up. The molecules move faster and spread out, so the balloon becomes bigger. This is an example of Charles’s Law.
Tyre Pressure Rising: When you drive, your tires get warm from rubbing against the road. The air inside heats up, the molecules move faster, and the pressure inside the tire increases. This is explained by Gay-Lussac’s Law.
Aerosol Cans Safety: If you heat or crush a pressurized spray can, the pressure inside can become dangerously high and cause the can to burst. This is because of the pressure-volume and pressure-temperature relationships in Boyle’s and Gay-Lussac’s Laws.
Hot Air Balloons Lift: Heating the air inside the balloon causes it to expand and become lighter (less dense) than the cooler air outside. Because hot air rises, the balloon lifts off the ground.
Breathing Mechanism: When you breathe in, your chest expands and increases the volume in your lungs, which lowers the pressure and pulls air in. When you breathe out, the volume decreases, pressure goes up, and air is pushed out. This breathing cycle is a natural example of Boyle’s Law in the human body.