Question

At NTP, the density of a gas, whose molecular weight is 45, is
A. 44.8g/L
B. 11.4g/L
C. 2g/L
D. 3g/L

Answer 1

Hint: We all know that density is one of the most important characterizations of the pure substance. Also, the formula of density is Mass/Volume. At NTP, the standard volume is equal to 22.4L.

Complete step by step solution:
We all know,the general meaning of density is the amount of substance per unit volume. Density is more precisely known as the “mass density”. Density can be expressed in any combination of mass and volume units. The most commonly used units are grams per mL ($\text{gm}{{\text{L}}^{-1}}$,$\text{gc}{{\text{m}}^{-3}}$ ) or kilograms per liter.
The density of any substance is calculated as
$\text{Density=}\dfrac{\text{Mass}}{\text{Volume}}$
Also, NTP stands for Normal Temperature and Pressure. In this condition
Normal temperature is \[{{20}^{\text{o}}}\text{C}\]or \[293.15\text{K}\] or ${{68}^{\text{o}}}$F.
Normal pressure is 1 atm or 101.325kPa or 760 mmHg (or torr) or 14.6959 psi.
The volume of gases is usually calculated at Normal temperature and pressure and is equal to 22.4L.
The mathematical calculation is mentioned below-
$\text{Density=}\dfrac{\text{Mass}}{\text{Volume}}$
\[\text{At NTP, Density=}\dfrac{\text{Molar Mass of Substance}}{\text{Volume at NTP}}\]
\[\dfrac{45}{22.4}=2.008\text{g/L}\]
Therefore, the density of gas whose molecular weight is 45 is option (c) 2g/L

Note: We all should know how temperature affects the density. All substances tend to expand as they are heated, causing the same mass to occupy a greater volume, and thus lowering the density. For most solids, this expansion is relatively small, but it is far from negligible. For liquids, it is greater. The volume of gases is highly temperature sensitive and so their densities.