Lesson 4: Ideal Gas Law
This lesson combines all the
properties of gases into a single
equation.
Ideal Gas Law
Combining Boyle’s and Charles’ laws allows for
developing a single equation:
P*V = n*R*T
P = pressure
V = volume
n = number of moles
R = universal gas constant (we’ll get to that in a
minute…)
T = temperature
Ideal Gas Law
P*V = n*R*T
This is one of the few equations in chemistry that you
should commit to memory!
By remembering this single equation, you can predict
how any two variables will behave when the others are
held constant in an IDEAL GAS
Gas Constant



The Ideal Gas Law as presented
includes use of the Universal Gas
Constant.
The value of the constant depends
on the units used to define the
other variables.
Usually: 0.0821 L*atm/mol*K
Practice




How many moles of a gas at 100⁰C
does it take to fill a 1.00 L flask to a
pressure of 1.50 atm?
PV=nRT
(1.50 atm)(1.00 L) = n(0.0821
atm*L/mol*K)(373 K)
n = 0.0490 mol
Ideal Gas Law: Summary

P*V = n*R*T



Learn it!
Use it!
This single equation can be used to
predict how any two variables will
behave when the others are held
constant.
Another Example – Using mass

Calculate the volume (in L)
occupied by 7.40 g of NH3 at STP.



Moles = 7.40 g /17 g (MM) = 0.44 mol
Plug into PV = nRT
Or the easier way!!!
You know at STP, a gas takes up 22.4 L
 So 0.44 mol x (22.4 L / 1 mol) = 9.74 L

PV = nRT ….x 2!

A small bubble rises from the bottom of a lake,
where the temperature and pressure are 8°C and
6.4 atm, to the water’s surface where the
temperature is 25°C and the pressure is 1.0 atm.
Calculate the final volume (in mL) of the bubble if
its initial volume was 2.1 mL.

We have two pressures, two temperatures, and one
volume (with the other one we need to find)
 P1V1
n1T1


P2V2
n2T2
R is left out since it’s the same on both sides and will
cancel itself out!
Technically, Boyle’s and Charles’ Laws are this equation
PV = nRT…x 2!!!





Now, we just plug everything in (assume
n stays constant since it’s not mentioned)
P1 = 6.4 atm, V1 = 2.1 mL, T1 = 281 K
P2 = 1.0 atm, V2 = ?, T2 = 298 K
(6.4*2.1)/281 = (1.0x)/298
x = 14 mL
Double PV=nRT Example #2

A gas initially at 4.0 L, 1.2 atm, and
66°C undergoes a change so its final
volume and temperature are 1.7 L
and 42°C, respectively. What is the
final pressure assuming the number
of moles remains unchanged?
Density Calculations



We can rearrange the ideal gas equation
to find density or molar mass:
PV = nRT, and n = mass (m)/MM (M)
Rearrange PV = nRT…


Substitute in m/M


(n/V) = P/RT
m/MV = P/RT
Since density is mass/volume….

D = PM/RT
Example

Calculate the density of CO2 in g/L at
0.990 atm and 55°C.



d = PM/RT
d = (0.990 atm)(44.01 g/mol) / (0.0821
L*atm/mol*K)(328 K)
d = 1.62 g/L
Non-Ideal Gases

Ideal gas law does NOT describe
gases in everyday behavior



PV=nRT also called the kinetic
molecular theory
We use it as an approximation
When do gases not obey the ideal
gas law:


1. High pressure
2. Very Low temperatures
Ideal Gases don’t exist

Molecules do take up space


All matter has volume
There are attractive forces

otherwise there would be no liquids
Real Gases behave like Ideal Gases




When the molecules are
far apart
They take a smaller
percentage of the space
Ignoring their volume is
reasonable
This is at low pressure
Real Gases behave like Ideal gases
when





When molecules are moving fast.
Molecules are not next to each other
very long
Attractive forces can’t play a role.
At high temp.
Far above boiling point.
Effect of Pressure
Molecule size
because they
are close
together
Intermolecular forces
stick molecules
together
17
Effect of Temperature
18
Van der Waal’s equation
2

 n
 P obs + a    x  V - nb   nR T


V




a is a number that depends on how
much the molecules stick to each other
– constant that corrects for pressure
b is a number that determined by how
big the molecules are – constant that
corrects for volume
19
Real Gas Example (van Der
Waals)


Given that 3.50 mol of NH3 occupy 5.20 L at
47°C, calculate the pressure of the gas using
(a) the ideal gas equation and (b) the van der
Waals equation)
(a) PV = nRT


P(5.20 L) = (3.50)(0.0821)(320 K)
P = 17.7 atm
Real Gas Example (van Der
Waals)


Given that 3.50 mol of NH3 occupy 5.20 L at
47°C, calculate the pressure of the gas using
(a) the ideal gas equation and (b) the van der
Waals equation)
(b) [P+ (an2/V2)](V-nb) = nRT




a = 4.17 atm*L2/mol2
b = 0.0371 L/mol
[P +(4.17*(3.502))/(5.202) = (3.50)(0.0821)(320)
P = 16.2 atm