# The Gas Laws and Stoichiometry

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The Gas Laws and Stoichiometry
Honors Option for Chemistry The Gas Laws and Stoichiometry

Kinetic Model of Gases The Big Variables are P, V and T
P is created by molecules colliding with the walls of the container

T is proportional to the average kinetic energy
V is the space allowed for the gas: remember gases are compressible T is proportional to the average kinetic energy

Boyle’s Law At a certain, fixed temperature the volume of a gas is proportional to the inverse of the pressure.

Charles’ Law Under constant pressure, as the temperature of a gas increases so does the volume

Gay-Lussac’s Law Under constant volume, the pressure and temperature are proportional

Avogadro’s Law Equal volumes of gases at the same temperature and pressure have the same number of molecules

Which Law is It?

Combined Gas Law So, why struggle to remember
all those people and laws when We can summarize them With the combined gas law. This law can be used to solve Problems with ANY of the Boyle-Charles-Gay-Lussac Conditions. Just leave out the Variable that is constant And only 1 law to remember!

Using the Ideal Gas Law What is an ideal gas?
How do gases deviate from the ideal? No gas is really ideal. However, this law gives good approximation of gas behavior. It does not work well when the temperature is low (near boiling point) or when the Pressure is high. Both of those conditions mean that the particles are very close Together and will experience forces between them. Molecules with high molar masses Also tent away from the ideal.

PV =nRT The ideal gas law!
This law uses the relationships from the combined law and add molar ratio This is often used to find molar mass or density Remember that molar mass is g/mole so g/n And density is mass/volume n/V x g/mole (molar mass)

Which Law to Use? P1V1 = P2V2 T1 T2 PV = nRT Conditions are changing Example: A piston (volume changes as it moves in and out) A balloon moving up in the atmosphere (the outside P decreases) Conditions are constant But one variable is unknown Finding the number of moles of a gas at known temperature, volume and pressure (STP for one) Finding any variable for a given chemical reaction

Stoichiometry Combined with Gas Laws
Example: For the reaction: 2H2 + O2  2H2O How many liters of oxygen are needed to react with 2.56 moles of hydrogen at STP? Find the moles of O2 needed. Use the molar ratio. 2.56 moles mole = moles O2 2 moles Change the moles to liters Sub into PV = nRT V = nRT/P V = (1.28 moles)( L atm/Kmol)(273K)/(1atm) V = L; with sig figs 28.7 L

An unknown gas has a density of 0. 89 g/ml at a pressure of 0
An unknown gas has a density of 0.89 g/ml at a pressure of atm and temperature of 25 C. What is the molar mass? Use PV = nRT molar mass = g/mol n/V = P/RT sub in n/V = (0.900 atm)/( Latm/Kmol)( K) n/V = mol/L We want g/mol for molar mass 0.89 g x ml x 1 L = g/mol ml L mol