What is the density of one mole of $\mathrm{He}$ (molar mass $=4 \mathrm{~g}$ $\left…

What is the density of one mole of $\mathrm{He}$ (molar mass $=4 \mathrm{~g}$ $\left.\mathrm{mol}^{-1}\right)$ at $300 \mathrm{~K}$ and a pressure of $0.82 \mathrm{~atm} ?(\mathrm{R}=0.082 \mathrm{~L}$ $\left.\operatorname{atm} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$
  1. $1.33 \times 10^{-2} \mathrm{~g} \mathrm{~mL}^{-1}$
  2. $1.33 \times 10^{-2} \mathrm{~g} \mathrm{~L}^{-1}$
  3. $1.33 \times 10^{-1} \mathrm{~g} \mathrm{~L}^{-1}$
  4. $1.33 \times 10^{-1} \mathrm{~g} \mathrm{~mL}^{-1}$

Solution

From ideal gas equation, $\mathrm{PV}=\mathrm{nRT}$ or, $\mathrm{PM}=\mathrm{dRT}$ $[\mathrm{d}=$ density of gas and $\mathrm{M}=$ molecular/atomic weight of the gas] $\therefore \quad \mathrm{d}=\frac{\mathrm{PM}}{\mathrm{RT}}$ $=\frac{0.82 \times 4}{0.082 \times 300}=\frac{4}{30}=1.33 \times 10^{-1} \mathrm{gL}^{-1}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

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