1. Gas Laws
Chapter 10

2. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. 2

3. P and V are inversely proportional
A plot of V versus P results in an inverse graph
Therefore is the pressure is doubled, the volume will be halved. 3

4. Boyle’s Law Practice Problem
If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?
P1V1 = P2V2
(1.5 atm)(5.6 L) = (x)(4.8 L)
x = 1.8 atm

5. Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature in Kelvins.
i.e., V T
= k
A plot of V versus T will be a straight line. 5

6. Charles’s Law Practice Problem
If I have 45 liters of helium in a balloon at 250 C and increase the temperature of the balloon to 550 C, what will the new volume of the balloon be?

7. Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
V1/n1 = V2/n2
Mathematically, this means
V = kn 7

8. Avagadro’s Law Practice Problem
A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas? Vf = (6.0 L x 0.75 moles)/0.5 moles Vf = 4.5 L/0.5 Vf = 9 L

9. Ideal-Gas Equation V  nT P So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
Combining these, we get
V  nT P 9

10. Ideal-Gas Equation
The constant of proportionality is known as R, the gas constant. 10

11. Ideal-Gas Equation PV = nRT nT P V  nT P V = R or The relationship
then becomes or
PV = nRT 11

12. Ideal Gas Law Practice Problem
If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 L, what is the temperature?
PV=nRT
205 K

13. Densities of Gases n P V = RT
If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT = 13

14. Densities of Gases n   = m P RT m V = We know that
moles  molecular mass = mass
n   = m
So multiplying both sides by the molecular mass ( ) gives P RT m V = 14

15. Densities of Gases P RT m V = d =
Mass  volume = density
So, P RT m V =
d =
Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas. 15

16. Molecular Mass P d = RT dRT P  =
We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT
d =
Becomes
dRT P
 = 16