Molar volume of $H e$ at $10.1325 M P a$ and $273 K i s 0.011075$ times its molar volume at $101.325 k P a$ . Calculate radius of $H e$ atom assuming negligible ' $a$ '. $(i n p m)$

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Solution

$P (V - b) = R T$
$101.325 (V - b) = R \times 273$ ......(1)
$10132.5 (0.011075 V - b) = R \times 273$ .....(2)
Divide equation (1) by equation (2)
$\frac{101.325 (V - b)}{10132.5 (0.011075 V - b)} = \frac{R \times 273}{R \times 273}$
$101.325 (V - b) = 10132.5 (0.011075 V - b)$
$(V - b) = 100 (0.011075 V - b)$
$V - b = 1.1075 V - 100 b$
$99 b = 0.1075 V$
$b = 0.0010858 V$ .....(3)
Substitute (3) in (1)
$101.325 (V - 0.0010858 V) = 8.314 \times 273$
$V = 22.4 d m^{3} = 22400 c m^{3}$
$r = (V \times \frac{3}{4 N Π})^{1 / 3} r = (22400 \times \frac{3}{4 \times 6.023 \times 10^{23} \times 3.1416})^{1 / 3} = 2.07 \times 10^{- 7} c m = 2070 p m$

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