DISCUSSION
Central goal:
To apply the particulate model of matter to determine the relative mass of different particles, as well as the number of particles present in any given sample of a substance.

Modeling is a powerful tool not only to explain and make predictions about the properties of substances, but to guide the experimental determination of such properties.
In lecture, you have been analyzing the particulate model of matter.
How can we use it to derive properties useful in the identification of unknown substances?

At low P and T much higher than their boiling point, the behavior of many gases can be modeled assuming that the system is composed of moving, non interacting particles.
Why?

P
What does the ideal gas model predict?
P P n V
P a
T
T
P a n P a
1/V
This “ideal” behavior of gases is described by the following relationship:
Proportionality
R

Constant atm L
0 .
082057 mol K
P

R nT
V
Equation of State

P

R nT
V
The number of moles in a real sample can be expressed in terms of the molar mass ( M
NA
) of the substance: n

M
M
N
A
Total mass
Molar Mass
P

MT
R
M
N
A
V
M
N
A

R
MT
PV
This relationship could be used to determine M
NA for a substance
(a differentiating characteristic) based on the measurement of
P , T , V , and M for a sample of gas.

Let ′s Think!
M
N
A

R
MT
PV
R

0 .
082057 atm L mol K
The following table summarizes data for an experiment designed to determine the molar mass of a gaseous substance:
M T
0.1034
g 20.0
o C
P
671.
mm Hg
V
20.0 mL
1 atm = 760 mm Hg a) Determine the molar mass of this substance, and b) the # of moles and c) the
# of molecules involved in the experiment?

M
N
A

R
MT
PV
R

0 .
082057 atm L mol K
M
0.1034
g
T
20 o C
293.15
K
P
671 mm Hg
0.883
atm
V
20.0 mL
0.0200
L
M
N
A

R
MT
PV

0 .
082057 x
0 .
1034 x 293 .
15
0 .
883 x 0 .
0200

141.
g/mol n

M
M
N
A

0 .
1034
141 .
g / g mol

7.33 x 10 -4 mol
N
 nN
A

7 .
33 x 10

4 x 6 .
022 x 10
23 
4.42 x 10 20 molecules

M
N
A

R
MT
PV
Let ′s Think!
R

0 .
082057 atm L mol K
Imagine that you use acetone ( C
3
H
6
O ) as your reference liquid to verify the accuracy of your experimental technique to determine molar masses.
a) What is the minimum volume of acetone (in mL ) that you should boil and transform into a gas if you use a 250.
mL flask as a container
( T = 20 o C, P = 671 mm Hg) b) How many moles of acetone is this?
c) How many molecules is this?
r
( C
3
H
6
O ) = 0.785
g/mL

Let ′s Think!
m
NA
58.08 g/mol
T
20 o C 671
P mm Hg
293.15
K 0.883
atm
V
250. mL
0.250
L
M

PVM
N
A
RT

0 .
883 x 0 .
250 x 58 .
08

0 .
082057 x 293 .
15
0.533
g
V

M r

0 .
533
0 .
785

0.679
mL n

M
M
N
A

0 .
533

58 .
08
9.18 x 10 -3 mol
N
 nN
A

9 .
18 x 10

3 x 6 .
022 x 10
23 
5.53 x 10 21 molecules