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Putting it all together: The Ideal Gas Law. We can combine the relationships stated in the three laws to create a single equation that will allow us to predict the pressure, volume or temperature of a certain number of moles of gas V=n(constant/P V=n(constant)T P=n(constant)T

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putting it all together the ideal gas law
Putting it all together: The Ideal Gas Law
  • We can combine the relationships stated in the three laws to create a single equation that will allow us to predict the pressure, volume or temperature of a certain number of moles of gas

V=n(constant/P

V=n(constant)T

P=n(constant)T

PV=n(constant)T

the ideal gas law
The Ideal Gas Law

PV=nRT where R=8.314 J/Kmol

  • The ideal gas law is an equation of state, an equation that describes the pressure, volume and temperature of a certain amount of a substance
  • We can use the equation by itself or we can use it to determine the properties of an ideal gas at 2 sets of conditions by using the combined gas law

4 6 gas density
4.6: Gas Density

We need to define a couple of terms and identify a couple of constants:

  • SATP: Standard Ambient Temperature and Pressure
    • 25 °C (298.15 K) and exactly 1 bar
  • STP: Standard Temperature and Pressure
    • 0 °C (273.15 K) and exactly 1 bar

At STP, Vm of ideal gases is 22.4 L/mole

At SATP, Vm of ideal gases is 24.79 L/mole

molar concentration
Molar Concentration
  • In Section G of the Fundamentals, we defined Molarity (M) as the
  • For a given pressure and temperature, the molar concentration should be the same for any gas
  • Two equal volumes of 2 different gases at the same temperature and pressure will contain the same # of molecules.
    • It doesn’t matter if the gasses are the same or different
gas density
Gas Density
  • One important, and difficult to grasp corollary to this:

If the molar masses are different, the two gas samples will have different masses.

  • For example: A balloon filled with helium at STP is lighter than the same balloon filled with Argon at STP. But they have the same number of molecules!
gas density1
Gas Density
  • Remember that the density of a gas is the mass divided by the volume
  • Gas density is usually expressed a g/L

The higher the molar mass, the higher the density

gas density summary
Gas Density: Summary

The molar concentrations and densities of gases increase as they are compressed (less volume, right?), but decrease as they are heated (volume increases, right?). The density of a gas depends on its molar mass.

the stoichiometry of reacting gases
The Stoichiometry of Reacting Gases
  • Many reactions occur in the gas phase and we can use the ideal gas law to determine the volume of gas produced or consumed in a chemical reaction
    • How much oxygen will it take to saturate the hemoglobin molecules in a red blood cell?
slide9

Steps to working with stoichiometry in the gas phase:

Balance the chemical equation

Calculate the number of moles of reactant consumed

Use the stoichiometric coefficients from the chemical reaction to relate the # moles of product made to the # of moles of reactant consumed.

mixtures of gases
Mixtures of Gases
  • Most gases we encounter and use every day are actually mixtures
    • The atmosphere of the earth
    • The breath we exhale
  • If the gases in a mixture do not react with each other, we may consider the mixture to be a single, pure gas for the sake of computation
mixtures and partial pressures
Mixtures and Partial Pressures
  • Dalton came up with the law that allows us to calculate the pressure of a mixture and the contribution of the individual gases that comprise it
  • How did he arrive at this conclusion?
  • He determined that if he combined the gases, the pressure of the mixture would be the sum of the Partial Pressures of the individual gases. And it is.
dalton s law of partial pressures
Dalton’s Law of Partial Pressures
  • The total pressure of a mixture of gases is the sum of the partial pressures of its components
mole fractions
Mole Fractions
  • The best way to explain/understand the relationship between total pressure and partial pressures is to look at the mole fractions of each gas in a mixture
  • For a mixture of gases with components A, B and C, the mole fraction (xA) is:
mole fractions1
Mole Fractions
  • We know that xA + xB + xC = 1
  • Each gas exerts a pressure that is the mole fraction of the gas times the total pressure in the vessel

PA = xAP