Ideal Gas Law Equations Calculator

Science Physics Chemistry Formulas

ideal gas law equation
Universal Gas Constant:
Universal Gas Constant

Problem:

Solve for pressure:

pressure

Enter Inputs:

moles (n)
temperature (T)
volume (V)

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Solution:

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Ideal Gas Law
pressurepressure
volumevolume
molemole
temperaturetemperature
Ideal Gas Law
densitydensity
pressurepressure
specific gas constantspecific gas constant
temperaturetemperature
Boyle's Law
Boyle's law equation or formulaBoyle's Law
Boyle's Law equation arranged to solve for pressure at state 1pressure at state 1
Boyle's Law equation arranged to solve for volume at state 1volume at state 1
Boyle's Law equation arranged to solve for pressure at state 2pressure at state 2
Boyle's Law equation arranged to solve for volume at state 2volume at state 2
Where
P=pressure
V=volume
n=mole
R=universal gas constant
T=temperature
ρ=density
Rspecific=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.
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