P20 087

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87.

(a) Since n/V = p/RT , the number of molecules per unit volume is

N

V

=

nN

A

V

= N

A



p

RT

 

6.02

× 10

23



1.01

× 10

5

Pa



8.31

J

mol

·K



(293 K)

= 2.5

× 10

25

molecules

m

3

.

(b) Three-fourths of the 2.5

× 10

25

value found in part (a) are nitrogen molecules with M = 28.0 g/mol

(using Table 20-1), and one-fourth of that value are oxygen molecules with M = 32.0 g/mol.
Consequently, we generalize the M

sam

= N M/N

A

expression for these two species of molecules and

write

3

4



2.5

× 10

25



28.0

6.02

× 10

23

+

1

4



2.5

× 10

25



32.0

6.02

× 10

23

= 1.2

× 10

3

g .


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