Question

What are the units of Vanderwaals constants `a' and `b' ?

Answer 1

Vander Waals Equation,

(P+an²/V²)(V- nb) = nRT

Where, Pa= an²/V²  (Pa is the internal pressure of gas, V is the volume, T is temperature)

Then, a=P ˣ V²/ n²= Pressure ˣ (Volume)²/(Moles)²

Unit of "a"  and  is atm lit² mol⁻²

Unit of "b" liter mol⁻¹

Answer 2

Unit of a is $atm.dm^{ 6 }.mo{ l }^{ -2 }$ and unit of 'b' is ${ dm }^{ 3 }.$${mol }^{ -1 }$

The pressure produced by the attractive force is proportional to the square of the number density.  

The Vander Waal's equation is given below,

            $\left( P\quad +\quad \frac { a }{ { V }^{ 2 } } \right) (V\quad -\quad b)\quad =\quad RT$

P = Pressure

V = Volume

T = Temperature

'a' and 'b' are constants.

            $The\quad unit\quad of\quad 'a':$

            $P\quad +\quad a\frac { { n }^{ 2 } }{ { V }^{ 2 } }$

            $a\quad =\quad \frac { P{ V }^{ 2 } }{ { n }^{ 2 } }$

            $a\quad =\quad \frac { atm.(d{ m }^{ 3 }{ ) }^{ 2 } }{ (mol{ ) }^{ 2 } }$

            $a\quad =\quad atm.\quad dm^{ 6 }.\quad mo{ l }^{ -2 }$

            $The\quad unit\quad of\quad 'b':$

            $\frac { V }{ n } \quad -\quad b$

            $b\quad =\quad \frac { V }{ n }$

            $b\quad =\quad { dm }^{ 3 }{ .mol }^{ -1 }$