Ideal Gas Law

Core Concept

The Ideal Gas Law is an equation that combines the relationships between pressure, volume, temperature, and the number of moles of a gas. It provides a way to predict and calculate these properties for an ideal gas.

  • Check Units: Make sure to convert all units appropriately (e.g., pressure in atm, temperature in K).

  • Rearrange First: Rearrange the Ideal Gas Law to isolate the desired variable before plugging in numbers.

  • Use Kelvin for Temperature: Convert Celsius to Kelvin to ensure accuracy.

  • Know When to Use It: The Ideal Gas Law is best used when dealing with typical gas conditions (not extremely high pressures or low temperatures).

Test Yourself

Assorted Multiple Choice
A constant current is passed through an electrolytic cell for 45.0 minutes, delivering a total charge of 8,100 Coulombs. How many moles of electrons were transferred during this process? (Faraday's constant = 96,485 C/mol e⁻)

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Ideal Gas Law

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Ideal Gas Law Equation

The Ideal Gas Law is expressed as: PV=nRT

Where:

  • P = Pressure of the gas (in atmospheres, atm)

  • V = Volume of the gas (in liters, L)

  • n = Number of moles of the gas (in moles, mol)

  • R = Ideal gas constant, $0.0821 \, \text{L} \cdot \text{atm} \, \text{K}^{-1} \, \text{mol}^{-1}$

  • T = Temperature of the gas (in Kelvin, K)

Key Terms

  1. Universal Gas Constant, R:

    • The ideal gas constant, R, is used to relate all units in the equation and has a value of $0.0821 \, \text{L} \cdot \text{atm} \, \text{K}^{-1} \, \text{mol}^{-1}$ when pressure is in atmospheres.

  2. Temperature in Kelvin:

    • Temperature must always be in Kelvin (K) for gas law calculations. To convert from Celsius to Kelvin, use: T (K) = T(°C) + 273.15

  3. Units Matter:

    • The units for P, V, and T must match the units in the ideal gas constant R to ensure accurate calculations.

    • Typically: P in atm, V in L, T in K, and nnn in moles.

  4. Applicability of the Ideal Gas Law:

    • The Ideal Gas Law applies well to ideal gases, which follow all gas laws perfectly under typical conditions.

    • Real gases approximate ideal behavior at high temperatures and low pressures, where gas molecules are far apart.

Rearranged Forms of the Ideal Gas Law

The Ideal Gas Law can be rearranged to solve for any variable when the others are known:

  1. To Find Pressure:

    $P = \frac{nRT}{V}$

  2. To Find Volume:

    $V = \frac{nRT}{P}$

  3. To Find Moles:

    $n = \frac{PV}{RT}$

  4. To Find Temperature:

    $T = \frac{PV}{nR}$

Video Resources

A man with curly hair and a beige shirt standing in front of a white background with the word 'DENSITY' in large purple letters behind him.
A whiteboard with the equation for density written in black marker: Density = Mass / Volume.