The behaviour of gases can be explained by mathematical relationships. The Ideal Gas Equation is one of the most basic laws governing gases. It helps us to understand how gases respond to changes in pressure, volume, and temperature.
Ideal Gas Equation
The ideal gas equation is given by: PV = nRT
where:
P = Pressure of the gas (in pascals, Pa)
V = Volume of the gas (in cubic meters, m³)
n = Number of moles of the gas
R = Universal gas constant (8.314 J/mol·K)
T = Temperature (in Kelvin, K)
This equation combines Boyle’s Law, Charles’s Law, and Avogadro’s Law into a single relationship.
Ideal Gas Equation and Absolute Temperature
Components
1. Pressure (P): The force exerted by gas molecules per unit area. It is measured in pascals (Pa) or atmospheres (atm).
2. Volume (V): The space occupied by the gas. It is measured in cubic meters (m³) or liters (L).
3. Number of moles (n): The amount of gas present, given in moles.
4. Temperature (T): The measure of the average kinetic energy of gas molecules. It must always be in Kelvin (K) when using the ideal gas equation.
5. Gas Constant (R): A universal constant that ensures consistency in calculations.
Temperature on any scale can be converted into the other scale using the following formula:-
Reading on any scale – Lower fixed point / Upper fixed point – Lower fixed point = Constant for all scales.
tC – 0 / 100 = tF – 32 / 212 – 32 = tg – 0 / 80 – 0 =
tg – 273.15 / 373.15 – 273.15
Importance of Absolute Temperature
Kelvin (K) scale serves as the foundation for the absolute temperature scale, with 0 K (absolute zero) being the lowest temperature. Since molecular motion stops at absolute zero, gas molecules have no kinetic energy.
Why we use Kelvin?
The Kelvin scale starts at absolute zero (0 K), which is a basic reference point in thermodynamics.
The temperature in gas laws must always be in Kelvin because gas behaviour is directly proportional to the absolute temperature.
Converting of Celsius to Kelvin is easy:
The formula for converting Celsius to Kelvin is:
K=°C+273.15 Where:
K is the temperature in Kelvin
°C is the temperature in Celsius
For example, if the temperature is 25°C, the equivalent in Kelvin is: 25 + 273.15=298.15K
Derivation of Ideal Gas Equation
The ideal gas equation is derived by combining three fundamental gas laws:
Boyle’s Law (P ∝ 1/V): At constant temperature, pressure and volume are inversely related.
Charles’s Law (V ∝ T): At constant pressure, the volume of a gas is directly proportional to its temperature
Avogadro’s Law (V ∝ n): At constant pressure and temperature, volume is directly proportional to the number of gas molecules.
By combining these relationships, we get:
The ideal gas equation is: PV = nRT
Where:
P = Pressure of the gas (in Pascals, atm, etc.)
V = Volume of the gas (in liters, cubic meters, etc.)
n = Number of moles of the gas
R = Universal gas constant (8.314 J/(mol⋅K) or 0.0821 L⋅atm/(mol⋅K)
T = Temperature (in Kelvin)
Applications of the Ideal Gas Equation
Weather Forecasting: Predicting weather patterns requires an understanding of variations in atmospheric pressure.
Engineering and Industry: It is applied to the design of airbags, engines, and freezers.
Medicine and respiration: It helps to understand the human body’s gas exchange and lung capacity.
Aerospace and Space Science: Helpful in figuring out the pressure and fuel needs in space.
Limitations of the Ideal Gas Equation
The formula makes the assumption that there are no intermolecular forces, or interactions, between gas molecules.
Low pressure and high temperatures defer the best accuracy. Real gases behave differently from ideal gases at high pressures and low temperatures.
The finite volume of gas molecules is not taken into account.
Note
An ideal gas formula describes how gases behave in various situation. All gas calculations are guaranteed to remain consistent and understandable, Kelvin provide the absolute scale. Despite its drawbacks, the equation provides a good approximation for the majority of gases in normal circumstances.
The ideal gas equation is a mathematical relationship that describes the behavior of an ideal gas. It is given by: PV = nRT
where: P = Pressure of the gas, V = Volume of the gas, n = Number of moles of the gas, R = Universal gas constant (8.314 J/mol·K)
T = Absolute temperature in Kelvin
Absolute temperature is the temperature measured on the Kelvin scale, where 0 K (absolute zero) is the lowest possible temperature. It is related to the Celsius scale as:
T(K) = T(0C) +273.15
Absolute temperature is important in gas laws because temperature must always be in Kelvin when using the ideal gas equation.
Because it makes predictions about how gases will behave under various pressure, volume, and temperature conditions, the ideal gas equation is essential to thermodynamics and chemistry. Environmental science, engineering, and physics all make extensive use of it.
The ideal gas law presupposes that gas particles do not exert attractive or repulsive forces and flow randomly.
• Gas-molecule collisions are completely elastic.
• In relation to the total gas volume, the volume occupied by gas molecules is insignificant.
• Under normal circumstances, the gas complies with all gas laws.
The ideal gas equation states that temperature is directly correlated with both volume and pressure. This implies that, assuming volume remains constant, pressure rises with temperature.
• If pressure remains constant, volume increases as temperature rises.
• Molecular mobility ceases and gases condense into liquids or solids as the temperature gets close to absolute zero (0 K).
The universal gas constant R has different values depending on the units used:
8.314 J/mol K 8.314 (SI unit)
0.0821 L\ atm / mol K0.0821(commonly used in chemistry)
62.36 L\mm Hg/mol K 62.36