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For one mole of a van der Waals gas when...

For one mole of a van der Waals gas when b=0 and T=300 K, the PV vs 1/V plot is shown below. The value of the van der Waals constant 'a' (atm `litre^(2)mol^(2)`) is

A

`1.0`

B

`4.5`

C

`1.5`

D

`3.0`

Text Solution

Verified by Experts

The correct Answer is:
C
van der Waals equation for 1 mole of real gas is
`(P+(a)/(V_(2)))(V-b)=RT`
But b=0 (Given). Hence,
`(P+(a)/(V_(2)))(V)=RT`
or `PV+(a)/(V)=RT`
or PV`=-(a)/(V)+RT` which is like `y=mx+c`.

Hence, plot of PV vs `(1)/(V)` is linear with slope`=-a`
Slope`=tan(pi-theta)=-a`
`:. tan theta=a(21.6-20.1)/(3-2)=1.5`
or `tan theta=(24.6-20.1)/(3-0)=1.5`
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