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If the slope of 'Z' (compressibility fac...

If the slope of 'Z' (compressibility factor) vs. 'p' curve is constant `("slope"=(pi)/(492.6)atm^(-1))` at a particular temperature (300 K) abd very high pressure, then calculate diameter of the molecules.
(Given : `N_(A)=6.0xx10^(23), R=0.0821 atm.Lmol^(-1)K^(-1)`)

A

7.5 Å

B

5 Å

C

2.5 Å

D

1.25 Å

Text Solution

Verified by Experts

The correct Answer is:
b
(b) `Z=1+(Pb)/(RT)` at high pressure
slope`=(b)/(RT)=(pi)/(492.6)`
`impliesb=(pi)/(492.6)xx0.0821xx300 and`
`b=(4)/(3)pir^(3)xx4N_(A)`
`=(pi)/(492.6)xx0.0821xx300xx10^(-3)`
`implies" "r=2.5 Å " or " d=5 Å`
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