Question

the van der waals equation for a gas is [p+a/v^2](V-b)=nRT where P,V,R,T and n represent the pressure,volume,universal gas constant,absolute temperature and number of moles of a gas respectively.a and b are constant .the ratio b/a will have the following dimensional formula
A)M-1L-2T2 B)M-1L-1T-1 C)ML2T2D)MLT-2

Answer 1

Answer:

Option A.

Explanation:

Vander Waal's Universal equation for a non ideal gas :

 ( P + a/v² ) * (V - b) = n R T

with the symbols having the given meanings.

P = pressure. V = volume. R = Universal Gas constant. T = absolute temperature. n = number of moles of the gas.

Since P has dimensions of Force/Area, a/V² also will have the same units and dimensions.

P = [ M ] [ L⁻¹ ] [ T⁻² ] = a / V² = a [ L³ ]⁻²

So constant a = [ M ] [ L⁵ ] [ T⁻² ]

Since b has same units and dimensions as that of V,

  b = [ L³ ]

Then the ratio b/a will have the dimensions:   [ M⁻¹ ] [ L⁻² ] [ T² ]

Answer is the option (A).