Calculate the pressure of one mole of nitrogen gas in a 10 L cylinder at $50^{\circ} C$ using the Van der Waal's equation.Also find the value of ideal gas pressure.(Van der Waal's constants a and b for nitrogen are $1.4 L^{2} a t m m o l^{- 2} a n d 0.04 L^{2} m o l^{- 1}$ respectively) .

Q. Calculate pressure exerted by 1 mole of a van der Waal gas at a temperature of

\frac{8}{0.0821} K

in a

\frac{1}{2} L

container, if the volume of the molecule is assumed to be negligible and van der Waal's constant

a = 2 {atm L}^{2} {mol}^{- 2}

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Calculate the radius of He atoms if its van der Waal's constant 'b' is 24 ml mol−1.

The correct option is A 1.355oAb=4× volume of 1 mole molecules b=4NA(43πr3)r=(3b16NAπ)1/3=(3×2416×6.023×1023×3.14)1/3=1.335×10−8cm=1.335oA

Calculate the radius of $H e$ atoms if its van der Waal's constant 'b' is $24$ ml mol $^{- 1}$ .

The correct option is A $1.355 o A$
$b = 4 \times$ volume of 1 mole molecules
$b = 4 N_{A} (\frac{4}{3} π r^{3})$
$r = (\frac{3 b}{16 N_{A} π})^{1 / 3} = (\frac{3 \times 24}{16 \times 6.023 \times 10^{23} \times 3.14})^{1 / 3} = 1.335 \times 10^{- 8} c m = 1.335 o A$