PV = nRT

Definition

The equation PV = nRT is known as the ideal gas law, which relates the pressure (P), volume (V), and temperature (T) of an ideal gas to the amount of substance in moles (n) and the ideal gas constant (R). This fundamental equation connects these variables, indicating how gases behave under varying conditions. Understanding this relationship is crucial for grasping concepts like gas pressure, temperature scales, and the speed of gas molecules.

5 Must Know Facts For Your Next Test

1. In the equation, P is measured in atmospheres (atm), V in liters (L), n in moles, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T in Kelvin (K).
2. The ideal gas law applies under conditions of low pressure and high temperature, where gas molecules behave ideally and intermolecular forces can be neglected.
3. The law can be rearranged to solve for any variable, allowing calculations for changes in pressure, volume, or temperature when one or more variables are altered.
4. When temperature increases at constant volume, pressure increases as well; this is a direct consequence of the kinetic theory of gases.
5. RMS speed can be derived from the ideal gas law using the equation $$v_{rms} = ext{sqrt}(\frac{3RT}{M})$$ where M is molar mass.

Review Questions

• How does the ideal gas law relate changes in pressure and volume to temperature in a closed system?
  • The ideal gas law shows that if the volume of a gas decreases while keeping the amount of substance and temperature constant, the pressure must increase. This relationship can be understood through Boyle's Law, which states that pressure is inversely proportional to volume at constant temperature. Therefore, any change to one variable will directly impact the others in a closed system.
• Analyze how the concept of absolute temperature is crucial for understanding the ideal gas law.
  • Absolute temperature is essential in the ideal gas law because it ensures that all calculations involving temperature reflect a scale where molecular motion stops at zero. Using Kelvin rather than Celsius or Fahrenheit allows for accurate relationships between pressure, volume, and temperature without negative values interfering with calculations. This consistency helps explain why gases expand when heated, as increased molecular activity leads to greater pressure or volume changes.
• Evaluate the implications of real gases deviating from ideal behavior and how this affects calculations using PV = nRT.
  • Real gases often deviate from ideal behavior under high pressure or low temperature due to intermolecular forces and finite molecular volume. This deviation means that PV = nRT may not hold true in these conditions, leading to inaccuracies in predictions. To address this, corrections such as the Van der Waals equation can be applied to account for interactions between gas molecules, providing a more accurate model of real gas behavior and ensuring that predictions align closer with experimental observations.

Related terms

Ideal Gas: A theoretical gas composed of many particles that are in random motion and do not interact with each other, behaving according to the ideal gas law.

Absolute Temperature: A temperature measurement on the Kelvin scale, starting from absolute zero, where all molecular motion ceases.

RMS Speed: The root mean square speed of gas molecules, representing the average speed of particles in a gas and related to temperature.