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  3. Chemistry
  4. A gas at 350 K 15 atm has a molar volume 12 percent smaller than that calculated from the perfect gas law. Compressibility factor under these conditions can be expressed in scientific notation as 88 × 10-x. The value of x is

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Q. A gas at $350\, K \,15 \,atm$ has a molar volume $ 12$ percent smaller than that calculated from the perfect gas law. Compressibility factor under these conditions can be expressed in scientific notation as $88 \times 10^{-x}$. The value of $x$ is ___

States of Matter

Solution:

$Z=\frac{P V_{ m }}{R T}=\frac{V_{ m }}{V_{ m } \text { perfect }}$
Given, $V_{ m }=V_{ m }$ perfect $-0.12 V _{ m }$ perfect
$=0.88 V _{ m }$ perfect
$Z =\frac{ V _{ m }}{ V _{ m } \text{perfect} }=0.88$
$=88 \times 10^{-2}$