Ideal Gas Law, formula, relationship

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The Ideal Gas Law is a fundamental equation in chemistry and physics that describes the behavior of ideal gases. It relates the pressure, volume, temperature, and number of moles of a gas.

Formula

The Ideal Gas Law is expressed by the equation:

\[ PV = nRT \]

Where:

  • \( P \) = pressure of the gas (usually in atmospheres, Pa, or mmHg)
  • \( V \) = volume of the gas (usually in liters or cubic meters)
  • \( n \) = number of moles of the gas
  • \( R \) = ideal gas constant (approximately 0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
  • \( T \) = absolute temperature of the gas (measured in Kelvin)

Relationships

  1. Pressure and Volume: At a constant temperature (isothermal condition), if the volume of the gas decreases, the pressure increases, and vice versa (Boyle's Law).

    \[ P_1 V_1 = P_2 V_2 \]

  2. Volume and Temperature: At a constant pressure (isobaric condition), if the temperature of the gas increases, the volume increases, and vice versa (Charles's Law).

    \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

  3. Pressure and Temperature: At a constant volume (isochoric condition), if the temperature increases, the pressure increases, and vice versa (Gay-Lussac's Law).

    \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

  4. Moles and Volume: Under constant temperature and pressure, the number of moles of gas is directly proportional to the volume (Avogadro's Law).

    \[ \frac{n_1}{V_1} = \frac{n_2}{V_2} \]

Notes

  • The Ideal Gas Law assumes ideal behavior of gases; real gases deviate from this behavior at high pressures and low temperatures.
  • The law applies generally well to many gases under standard conditions but may not accurately predict the behavior of gases in extreme conditions.
  • Remember to convert all units appropriately when applying the Ideal Gas Law. For example, convert degrees Celsius to Kelvin by adding 273.15.