Ideal Gas Law Equation Formula Calculator

Science Physics Chemistry Formulas

Universal Gas Constant:

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Ideal Gas Law

	pressure
	volume
	mole
	temperature

Ideal Gas Law

	density
	pressure
	specific gas constant
	temperature

Boyle's Law

	Boyle's Law
	pressure at state 1
	volume at state 1
	pressure at state 2
	volume at state 2

Where

P	=	pressure
V	=	volume
n	=	mole
R	=	universal gas constant
T	=	temperature
ρ	=	density
R_specific	=	specific gas constant

References - Books

Tipler, Paul A.. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.

Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

Background

We first must delve into the Ideal Gas Law to understand how to solve for pressure given volume, mole, temperature, and the universal gas constant. This law provides a clear relationship between these variables for an ideal gas, which is a hypothetical gas that perfectly follows the behavior described by the law without any deviation. Natural gases do not adhere entirely to this law, but they are an excellent approximation under various conditions.

Equation

The Ideal Gas Law is mathematically represented as:

PV = nRT

Where:

P - gas pressure
V - volume occupied by the gas
n - represents the number of moles of the gas
R - universal gas constant, 8.314 J/mol·K or 0.0821 L·atm/mol·K
T - temperature of the gas in Kelvin

How to Solve

To solve for pressure (P) given volume (V), mole (n), temperature (T), and the universal gas constant (R), you can rearrange the Ideal Gas Law equation as follows:

P = nRT / V

This equation tells us that pressure is directly proportional to the quantity of moles and the temperature and inversely proportional to the volume.

Example

Suppose we have a 2.00 mol sample of a gas at a temperature of 300 K, occupying a volume of 0.50 L. Let’s calculate the pressure the gas exerts using the Ideal Gas Law.

Given:

n = 2.00 mol
T = 300 K
V = 0.50 L
R = 0.0821 L·atm/(mol·K) (assuming pressure is to be calculated in atm)

Substituting these values into the equation P = nRT / V, we have:

P = 2.00 mol x 0.0821 L·atm/(mol·K) x 300 K / 0.50 L = 98.52 atm

Thus, the pressure exerted by the gas is 98.52 atm.

Fields/Degrees it is used in

Chemical Engineering: For designing reactors and understanding gas reactions.
Aerospace Engineering: In studying the behavior of gases at different altitudes.
Meteorology: To predict weather patterns and study atmospheric conditions.
Environmental Science: In the study of greenhouse gas emissions and their effects.
Pharmacy: For the production of gases used in medical treatments.

Real-Life Applications

Calculating Atmospheric Pressure: Essential for weather predictions and understanding climate change.
Scuba Diving: For determining how much tanks can provide breathable air at different depths.
Designing Combustion Engines: To optimize fuel use and minimize emissions.
Food Packaging: To calculate the ideal gas mix for packaging to extend shelf life.
Space Exploration: In calculating the conditions needed for spacecraft propulsion systems.

Common Mistakes

Forgetting Units: It's crucial to convert all measurements to their proper units before solving.
Ignoring Temperature Scale: Always use the Kelvin scale for temperature, as the Ideal Gas Law does not directly apply to Celsius or Fahrenheit scales.
Mixing R Values: Ensure the value of (R) matches the unit system used for pressure.
Neglecting Real Gas Behavior: Deviations from ideal behavior can occur at high pressures or low temperatures.
Incorrect Math Operations: Consider division and multiplication carefully to avoid calculation errors.

Frequently Asked Questions

Can the Ideal Gas Law be used for all gases?
A1: While the Ideal Gas Law is a valid approximation, it does not perfectly predict the behavior of real gases under all conditions, especially at very high pressures or low temperatures.
Why do we use Kelvin for temperature?
A2: Kelvin is used because it is an absolute temperature scale. This means 0 K (absolute zero) is the point at which particles have minimal thermal energy.
What is the importance of the universal gas constant?
A3: The universal gas constant (R) bridges macroscopic and microscopic physics, describing the properties of gases in various units and contexts.
How does changing the volume affect pressure?
A4: Decreasing the volume while keeping the temperature and moles constant increases pressure due to molecules colliding more frequently with container walls.
Can I calculate the number of moles from the Ideal Gas Law?
A5: Yes, if you know the pressure, volume, temperature, and the universal gas constant, you can arrange the Ideal Gas Law to calculate the number of moles.

Ideal Gas Law Equations Calculator

Problem:

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References - Books

Background

Equation

How to Solve

Example

Fields/Degrees it is used in

Real-Life Applications

Common Mistakes

Frequently Asked Questions