Question

A plant virus is found to consist of uniform cylindrical particles of 150 $A$ in diameter and 5000 Å long. The specific volume of the virus is 0.75 cm³/g. If the virus is considered to be a single particle, find its molecular weight.

Answer 1

SOLUTION : [Method : To determine molecular weight of virus particle we first calculate the mass of a single particle, and then multiplying by Avogadro number. By means of specific volume the mass of a single particle is found out.]

Given, $r=150 \times 10^{-8} / 2 cm =75 \times 10^{-8} cm ;

$l=5000 \times 10^{-8} cm =5 \times 10^{-5} cm$

$\because \quad$ Volume of a cylinder $=\pi r^{2} l$

$\therefore \quad$ Volume of virus $=3 \cdot 14 \times 75^{2} \times 5 \times\left(10^{-8}\right)^{2} \times 10^{-5} cm ^{3}$

$= 8 \cdot 83 \times 10^{-17} cm ^{3}$

Mass of a single particle $=\frac{8 \cdot 83 \times 10^{-17}}{0.75} g$

Molecular weight of the virus particle

$=\frac{8 \cdot 83 \times 10^{-17} \times 6.02 \times 10^{23}}{0.75} g mol ^{-1}$

$= 7 \cdot 087 \times 10^{7} g / mole$