Some Basic Concepts of Chemistry - Result Question 46
####46. A plant virus is found to consist of uniform cylindrical particles of $150 \AA$ in diameter and $5000 \AA$ long. The specific volume of the virus is $0.75 cm^{3} / g$. If the virus is considered to be a single particle, find its molar mass.
(1999, 3M)
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Solution:
- Volume of one cylinderical plant virus $=\pi r^{2} l$
$=3.14\left(75 \times 10^{-8}\right)^{2} \times 5000 \times 10^{-8} cm^{3}=8.83 \times 10^{-17} cm^{3}$
$\Rightarrow$ Mass of one virus $=\frac{\text { Volume of a virus }}{\text { Specific volume }}$
$$ =\frac{8.83 \times 10^{-17} cm^{3}}{0.75 cm^{3} g^{-1}}=1.1773 \times 10^{-16} g $$
$\Rightarrow$ Molar mass of virus
$$ \begin{aligned} & =\text { Mass of one virus } \times \text { Avogadro’s number } \ & =1.1773 \times 10^{-16} \times 6.023 \times 10^{23} g \ & =70.91 \times 10^{6} g \end{aligned} $$
