Putting it all together: The Ideal Gas Law

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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
• 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

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

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
• 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
• 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 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

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
• 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?

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
• 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
• 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
• The total pressure of a mixture of gases is the sum of the partial pressures of its components
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 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