Gay
– Lussac measured the volumes of
gases before and after reactions.
- Law of Combining Volumes: When gases react, the volumes of the reactants and products, measured at equal temperatures and pressures, are always in whole number ratios.
John
Dalton measured the masses of gases
before and after reactions.
- Law of Multiple Proportions: The masses of elements that combine into compounds can be expressed in small whole number ratios.
Avogadro,
using the above information, related the volume
of the gas to the amount that is
present. He
divided Dalton’s mass ratios by the molar masses to obtain the mole ratios. These mole ratios were the same as Gay-Lussac’s
volume ratios.
- Avogadro’s Law: Equal volumes of all ideal gases, at the same temperature and pressure, contain the same number of molecules (V ∝ n).
The molar volume of a gas is the space occupied by 1 mol of the gas ↝ 22.4 L
molar volume = V/n
Putting
it All Together
We
know:
V ∝ T
(Charles’ Law),
V ∝ 1/P (Boyle’s Law),
V ∝
n (Avogadro’s Law)
∴ V ∝
nT/P → V
= RnT/P (remember, to replace a proportionality sign with an equal sign, we need to include a constant; R represents this constant)
PV = nRT (Ideal Gas Law)
The
value of the Ideal Gas Constant, R,
at STP:
R
= PV/nT
R
= 101.325 kPa(22.4 L)/1.00 mol(273 K)
R
= 8.314 kPaᐧL/Kᐧmol
ex.
A container holds 4.5 mol of a gas at SATP.
What is the volume of the container?
n
= 4.5 mol
PV = nRT
T
= 298.15 K 100.0
kPa(V) = 4.5 mol(8.314 kPaᐧL/Kᐧmol)(298.15
K)
P
= 100.0 kPa
V = 111.491 L
V = ? ∴
the volume is 110 L.
Homework
Ideal
Gas vs. Real Gases - read p. 561-562 & briefly summarize
Practice
p. 549 # 17, 18
Practice
p. 556 # 21-25
Answers:
