The Ideal Gas Law

The Simple Gas Laws study the effect of changing pressure, temperature and moles have on the variable of volume. Together all three Simple Gas Laws combine to give the Ideal Gas Law

The Simple Gas Laws

Boyle’s Law states that pressure and volume are inversely proportionally, which basically means they are opposites, at constant moles and temperature.

Charles Law states that volume and temperature are directly proportionally if pressure and moles are constant. So if one is high then the other is high and vice versa. 

Avogadro’s Law states that volume and moles are directly proportionally at constant pressure and temperature. So if one is high then the other is high and vice versa. 

Concept: Understanding PV = nRT, the Ideal Gas Law

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Gay-Lussac’s Law states that pressure and temperature are directly proportionally at constant volume and moles. So if one is high then the other is high and vice versa. 

Simple Gas Law Calculations

Sometimes we will be given two of the same variables such as volume, temperature, pressure or moles. In these cases, you will have to learn to manipulate the Ideal Gas Law to isolate the equation you need. 

Example: A sample of neon gas occupies 112 mL at 0.567atm. If the temperature remains constant, what is the volume (in L) at 1165 mmHg?  

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When manipulating the Ideal Gas Law you want your common set of variables on one side of your equation. 

Example: An engineer pumps air at 0oC into a mechanized piston-cylinder engine. If the volume measures 7.18 cm3 what will the new temperature be at 12.3 mL? 

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Manipulating the Ideal Gas Law can help us solve questions beyond our understanding of the Simple Gas Laws. 

Problem: A large plastic container holds 47.1 g of water vapor at a pressure of 1.12 atm. What is the new pressure if 12.1 g of water vapor is removed at constant temperature?

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If we are not given two of the same variables such as volume, temperature, pressure or moles then we just use the Ideal Gas Law

Problem: A steel tank has a volume of 592 L and is filled with 0.638 kg of hydrogen gas. Calculate the pressure of the gas if the temperature is 82 degrees Celsius.

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Ideal Gas Law and Chemical Reactions

We’ve dealt with gases on previous topics such as stoichiometry, where the gas was either a reactant or product. Now we can relate Stoichiometry to the Ideal Gas Law. 

For a stoichiometric question dealing with the Ideal Gas Law just focus on the KNOWN quantities and determine which portion of the ideal Gas Law you need to isolate. 

Example: Magnesium reacts with excess hydrochloric acid to form aqueous magnesium chloride and 26.7 mL of hydrogen gas at 25oC and 723 mmHg.

Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2 (g)

How many grams of magnesium reacted?

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When a gas is collected over water the total pressure is the partial pressures of the gas and of water vapor. To determine the correct answer you need to find the partial pressure of only the gas. 

Example: Acetylene (C2H2), an important fuel in wielding, is produced in the laboratory when calcium carbide (CaC2) reacts with water:

CaC2 (s) + 2 H2O (l) → C2H2 (g) + Ca(OH)2 (aq)

The pressure of acetylene collected over water is 729 torr while the volume was measured as 629 mL. If at 21oC the vapor pressure of the water is 29 torr, how many grams of acetylene were produced? 

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