# Van der waals equation question

Hi everyone,

Struggling with the following question - maths and physics never been my strongest subjects. Thanks in advance

1. An equation of state that has been used to model the behaviour of a fixed amount of a real gas is:
(P+a/v2)(v-b)=ZT
In the equation Z, a, b are constants, and P represents pressure, V = volume, T = temp. The constant Z depends on the amount of gas.
Consider what the dimensions of a and b are in terms of the fundamental quantities of mass (M), length (l), and time (t).

2. Q1: The dimensions of b are:
a) L3
b) L6
c) M.L-1.T-2
d) M-1.L.T2

Q2: The dimensions of a are:
a) L6
b) M.L5.T-2
c) M.L-1.T-2
d) M.L-5.T-1

Q3: The value of the constant Z could be expressed in terms of the unit:
a) W
b) W.N.s-1
c) N.J.K-1
d) J.K-1

3. According to std van der Waal's equantion Z is equivalent of R, therefore Q3 = D, not sure about the calculations for Q1 or Q2

Any help would be greatly appreciated.

Thanks

## The Attempt at a Solution

chemisttree
Homework Helper
Gold Member
Hi everyone,

Struggling with the following question - maths and physics never been my strongest subjects. Thanks in advance

1. An equation of state that has been used to model the behaviour of a fixed amount of a real gas is:
(P+a/v2)(v-b)=ZT
In the equation Z, a, b are constants, and P represents pressure, V = volume, T = temp. The constant Z depends on the amount of gas.
Consider what the dimensions of a and b are in terms of the fundamental quantities of mass (M), length (l), and time (t).

2. Q1: The dimensions of b are:
a) L3
b) L6
c) M.L-1.T-2
d) M-1.L.T2

I'll help you with this one since it is the easiest. Without just giving you the answer I will explain by analogy. The portion of the equation that contains b is (v-b), right? You are subtracting b from the volume.

Now here is the hint/analogy... Can you subtract gallons from miles? Gallons from degrees C? No. What must the units of b... err be?