Gas Pressure Formula is P = (n/V)RT which is derived from the ideal gas law. This formula assumes that the gas behaves ideally, meaning it obeys the ideal gas law without considering factors such as intermolecular attractions. Gas pressure is the measure of force exerted by gas molecules in a specific area.
In this article, we look into gas pressure formula, gas pressure formula for mixture of gases, factors affecting gas pressure, derivation of gas pressure, and some solved examples based on it.
What is Gas Pressure?
Gas pressure is the force exerted by gas molecules when they collide with an object’s surface. It is measured in units like pascals (Pa), kilopascals (kPa), atmospheres (atm), or bars.
Gas Pressure is a measurement of the average linear momentum of the moving molecules of a gas. It acts perpendicular to the wall and measures the force exerted by the gas on a particular area.
Ideal Gas Pressure Formula
The ideal gas pressure formula is given by the ideal gas law, which states that pressure multiplied by volume is equal to product of number of moles, universal gas constant and its temperature. It is stated as:
PV = nRT
Where:
- P is the pressure of gas
- V is the volume of gas
- n is the number of moles in gas
- R is the gas constant (also known as the universal gas constant)
- T is the temperature in Kelvin.
Gas pressure formula is derived from the ideal gas law, which relates pressure (P), volume (V), temperature (T), and number of moles of the gas (n) through the universal gas constant (R). The gas pressure formula is expressed as:
P = (n/V)RT
The SI unit of gas pressure is Pascal or kilopascal. The other commonly used units for gas pressure include atmosphere(atm), torr, pounds per square inch(psi), etc.
Gas Pressure Formula for Mixture of Gases
Total pressure of a gas mixture is the sum of the partial pressures of each individual gas component in the mixture. The formula for the pressure of a gas mixture is given by:
PTotal = P1 + P2 + P3 + …………. + Pi
OR
Where
Ptot is the total pressure, and Pi is the partial pressure of the individual gas.
The derivation of gas pressure formula involves the combination of Boyle’s Law, Charles’s Law, and Avogadro’s Law. The relation of these formulas are described below:
Boyle’s Law: According to Boyle’s Law, at constant temperature and number of moles, the volume of a gas is inversely proportional to its pressure. Mathematically, this is expressed as
V ∝ 1/P
Charles’ Law: According to Charles Law, at constant pressure and number of moles, the volume of a gas is directly proportional to its temperature. This relationship is given by
V ∝ T
Avogadro’s Law: According to Avagadro Law, at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles. This can be represented as
V ∝ n
By combining these three laws, we get:
V ∝ nT/P
Simplifying this expression, we arrive at the ideal gas equation:
PV = nRT
Where,
R is the ideal gas constant.
Therefore, the derivation of the gas law pressure formula (ideal gas equation) involves combining Boyle’s Law, Charles’s Law, and Avogadro’s Law to show the relationship between pressure, volume, number of moles, universal gas constant, and temperature in an ideal gas.
Factors Affecting Gas Pressure
Factors affecting gas pressure include the number of gas particles, volume, and container temperature. These factors influence gas pressure as follow:
- Number of Gas Particles (n): Increasing the number of gas particles in a container leads to more collisions with the walls, resulting in higher pressure. Conversely, reducing the number of particles decreases the gas pressure within the container.
- Volume (V): Decreasing the volume of a container causes gas particles to have less space to move around, leading to more frequent collisions with the walls and an increase in gas pressure. Increasing the volume will result in decreasing the pressure.
- Temperature (T): Increasing a gas temperature increases its particles kinetic energy. This results in faster particle movement, more collisions with the walls, and a higher gas pressure. Decreasing the temperature will result in reducing the pressure.
Gas pressure formula, derived from the ideal gas law (PV = nRT), is used in various applications, such as calculating the volume of gasses in cylinders, determining changes in pressure and temperature, and understanding the behavior of gasses under different conditions. Few of its uses are stated below:
- The gas pressure formula, PV = nRT, relates pressure (P), volume (V), number of moles (n), universal gas constant (R), and temperature (T) of an ideal gas.
- It is used to calculate the individual pressure of each gas in a mixture by multiplying the mole fraction of each gas by the total pressure.
- The formula is applied to determine the partial pressure of gasses in a mixture, where the total pressure is the sum of the individual partial pressures.
- The ideal gas equation plays a crucial role in understanding the behavior of gasses and is fundamental in various calculations involving gasses.
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Example 1: A sample of nitrogen gas occupies a volume of 8 L at 27°C. If the temperature is increased to 93°C without changing the pressure or amount of gas, what will be its new volume?
Solution:
To solve this problem using Charles’s Law, we can use the equation
V1/T1=V2/T2
Here,
V1 = 8 L and T1 = (27 + 273)K = 300 K,
while T2 = (93 + 273)K = 366 K, Putting the given values in the above formula we get:
8/300 = V2/366
Now, cross-multiply:
300 × V2 = 8 × 366
Divide both sides by 300:
V2 = (8 × 366)/300 = 9.76
Hence the new Volume is 9.76 L.
Example 2: At standard temperature (27°C), a sample of helium has a volume of 0.1 m³ when the pressure is 3 atm. When the pressure increases to 6 atm, what will be its new volume if the temperature remains constant?
Solution:
Boyle’s Law states that
P1V1 = P2V2
Here, P1 = 3 atm and V1 = 0.1 m³, while P2 = 6 atm and the temperature stays constant. We want to find V2
3 × 0.1 = 6 × V2
Now, divide both sides by 6:
V2 = 3 × 0.1/6 = 0.05 m³
Hence, the new volume is 0.05 m³
Question 1: Calculate the gas pressure, if there are 500 moles of gas molecules in a container at a temperature of 220 K and a volume of 40 L.
Question 2: If gas molecules exert a force of 300 N in an area of 50 m², what is the gas pressure?
Question 3: A 325-mL sample of nitrogen is at a pressure of 500 mm Hg. If the volume changes to 150 mL, calculate the final pressure.
Question 4: A 325-mL sample of nitrogen is cooled from 250°C until its volume is 275 mL. What is the final temperature?
Question 5: A sample of oxygen occupies a volume of 437 mL at 25°C and 735 mm Hg pressure. Calculate the volume at STP
What is the pressure of the gas?
The pressure of a gas is the force exerted per unit area and is measured in Pascals (Pa) or atmospheres (atm). It depends on factors like temperature and volume, following Boyle’s and Charles’s laws.
What causes gas pressure?
The constant motion of gas molecules causes gas pressure. When these molecules collide with the walls of a container, they exert force, creating pressure. The more frequent and energetic the collisions, the higher the pressure, influenced by temperature and volume.
How to calculate the volume of gas with pressure?
To calculate the volume of a gas, use the ideal gas law:
V = nRT/P
Where
- V is volume,
- n is the number of moles,
- R is the gas constant,
- T is the temperature in Kelvin, and
- P is pressure.
What is the unit of gas pressure?
The SI unit of gas pressure is Pascal. Some other common units of gas pressure include atmosphere, torr, pounds per square inch(psi), etc.
How do you calculate gas pressure?
Gas Pressure can be calculated using the following formula:
P = nRT/V
where,
- P is the pressure of the gas .
- V is the volume of the gas.
- n is the number of moles of the gas.
- R is the ideal gas constant, and
- T is the temperature of the gas.
What is the value of universal gas constant (R)?
The value of universal gas constant (R) is 8.314 J · mol-1 · K-1
What is the formula for total pressure of a gas?
Total pressure of a gas mixture is the sum of the partial pressures of each individual gas component in the mixture. Mathematically, it can be represented as:
Ptotal = P1 + P2 + P3 + ……. + Pi
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