Boyle's Law

QuickNotes

Boyle's Law: P₁V₁ = P₂V₂

• P refers to pressure measured in atmospheres (atm)
• V refers to volume measured in Liters (L)
• The pressures and volumes must be given in the same units on both sides of the equation. For example:

(4 atm)(2 L) = (8 atm) (1 L) 

(4 atm)(2 L) = (8 torr)(1 mL) 

• Notice that problems involving Boyle's law are not affected by temperature. To recognize that a problem involves Boyle's Law, notice that various data about pressure and volume will be given followed by a statement that temperature is constant. 
• Important Concept: Pressure and Volume are inversely proportional. This means that as pressure increases, volume decreases, and vice versa. 

Examples: 

Example 1: At a constant temperature, a gas has a volume of 7.4 L and a pressure of 5.7 atm. What is its pressure in mmHg when the volume is reduced to 4.6 L?
       
       1. First, find the new pressure (P2)  in atm.

(7.4 L)(5.7 atm) = (4.6 L)(x atm)

x = 9.16 atm = 9.2 atm

       2. Then, convert the pressure in atm into pressure in mmHg.

(9.2 atm)(760 mmHg)/(1 atm) 

= 6992 mmHg =  7.0 x 10² mmHg

Example 2: At an underground mine, miners are in an environment enduring extremely high amounts of pressure. How many liters of gas at STP must be compressed at sea level to fill the cavern with 2.00 x 10⁷ L of air at 20.0 atm?

At STP, pressure = 1 atm, so:

(2.00 x 10⁷ L)(20.0 atm) = (1 atm)(x L)

x = 4.00 x 10⁸ mmHg

To make sure you totally understand Boyle's Law, check out this review video!

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Boyle's Law Quiz