Question

A certain vapor obeys tge van der Waals equation with a=.56m^6Pa mole^-2. Its volume is 5.00x10-4m^3mole^-1 at 273 K and 3.0x10^6Pa. Calculate the value of the van der Waals constant b for this substance.

Answer 1

the equation is:

Van der Waal's Equation

Van der Waal's equation is expressed by the formula

P + a(n/V)2 = nRT/(V-nb)

where
P = pressure
V = volume
n = number of moles of gas
a = attraction between individual gas particles
b = average volume of individual gas particles
R = ideal gas constant =

8.314

m3 Pa K−1 mol−1

T = absolute temperature

we take n=1

plugging in the values

3x10^6 + 0.56(1/5x10^-4)² = 1*8.314*273/(5x10^-4 - b)

5x10^-4 - b= /5240000

b= 5x10^-4 - 4.33x10^-4

b= 6.7x10^-5 m3