BioPHYSICAL chemistry

The force exerted on the walls is equal to the mass times the acceleration, or equivalently,

the rate of momentum change. Since the pressure is equal to the force divided by the area, the

pressure, P, can be written as the rate of the total momentum change divided by the area:

P=Nm (^9) x^2 (db1.7)
The pressure is then proportional to the average of the square of (^9) x. Since the particles are
traveling in three dimensions, the average total velocity, , is given by the sum of the
squares of the three individual components:
(db1.8)
On average, each of these three components is equal, so the sum is just three times the
value for one component, and the total velocity can be written as:
(db1.9)
and the pressure (eqn db1.7) can now be written as:
(db1.10)
The number density Nis the product of the number of moles nand Avogadro’s number NA
divided by the volume, so the pressure can be rewritten as:
(db1.11)
Finally, dividing by the volume yields:
PVnNm= A (db1.12)

92

3

PNm

nN

V

==Am

9922

33

PNmNm== (^9) x

2 92

3

9922 = (^3) x
99992222 =++xyz
(^9) a 9
modified with two empirical constants, aand b, to accommodate both the
size of each gas molecule and interactions between the molecules, using
the van der Waals’ equation:

(1.20)

What are these new parameters and how are they related to the size and
interactions of the gas molecules? The first term of the equation appears

P

nRT

Vnb

a

n

V

=

−

−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

2

CHAPTER 1 BASIC THERMODYNAMIC AND BIOCHEMICAL CONCEPTS 11