upgrade

💏intro to chemistry review

D = PM/RT

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The equation d = PM/RT, known as the ideal gas law, is a fundamental relationship that describes the behavior of gases. It connects the density (d) of a gas to its pressure (P), molar mass (M), and the temperature (T) of the system, using the universal gas constant (R).

5 Must Know Facts For Your Next Test

  1. The equation d = PM/RT is used to calculate the density of a gas given its pressure, molar mass, and temperature.
  2. The equation is derived from the ideal gas law, PV = nRT, by rearranging the terms to solve for density.
  3. The molar mass (M) is a measure of the average mass of one mole of a substance, and is an important factor in determining the density of a gas.
  4. The universal gas constant (R) is a fundamental physical constant that has a value of 0.082057 L⋅atm⋅mol^-1⋅K^-1, and is used in the ideal gas law and the d = PM/RT equation.
  5. The equation d = PM/RT is particularly useful in the context of stoichiometry of gaseous substances, as it allows for the calculation of gas densities and molar masses.

Review Questions

  • Explain how the d = PM/RT equation is derived from the ideal gas law.
    • The ideal gas law, PV = nRT, relates the pressure (P), volume (V), amount of substance (n), and absolute temperature (T) of an ideal gas, using the universal gas constant (R). To obtain the d = PM/RT equation, we can rearrange the ideal gas law by solving for the density (d = m/V), where m is the mass of the gas and V is the volume. Substituting n = m/M, where M is the molar mass, we can arrive at the equation d = PM/RT, which connects the density of a gas to its pressure, molar mass, and temperature.
  • Describe how the d = PM/RT equation can be used to determine the molar mass of a gas.
    • The d = PM/RT equation can be rearranged to solve for the molar mass (M) of a gas, given the density (d), pressure (P), and temperature (T) of the system. By isolating M in the equation, we get M = dRT/P. This allows us to calculate the molar mass of a gas if we know its density, the pressure it is subjected to, and the temperature of the system. This can be particularly useful in the context of stoichiometry, where the molar mass of a gas is an important factor in determining the relationships between the amounts of reactants and products in a chemical reaction involving gases.
  • Explain how the d = PM/RT equation can be used to analyze the behavior of gas mixtures and reactions.
    • The d = PM/RT equation is crucial in the study of stoichiometry of gaseous substances and mixtures. By applying this equation, we can determine the densities of individual gases within a mixture, which is essential for understanding the composition and behavior of the mixture. Additionally, the equation can be used to analyze the changes in gas density that occur during chemical reactions involving gases, allowing us to better understand the relationships between the reactants and products in terms of their molar masses and the conditions (pressure and temperature) of the system. This understanding is vital for accurately predicting and interpreting the stoichiometry of gaseous reactions.