Question

The density of the gas is equal to:
A) ${\text{nP}}$
B) $\dfrac{{{\text{MP}}}}{{{\text{RT}}}}$
C) $\dfrac{P}{{{\text{RT}}}}$
D) $\dfrac{{\text{M}}}{{\text{V}}}$

Answer 1

Hint: In this question formulas related to the density are given. Density can be defined as mass per unit volume of a substance under explicit states of temperature and weight. So, one can relate this information to find out the mathematical formula for the density in given options.

Complete step by step answer:
1) First of all we will know the concept of density from which we can find out the expression for the same. The density is characterized as mass per unit volume of a substance under explicit states of temperature and weight. The density of the gas is equivalent to its mass partitioned by the volume.
2) As we need to get the mathematical formula for density, by using the gas equation we can find out the mathematical expression for density as follows,
\[PV = nRT\]
Where $n = $ the number of moles. As we know $n = \dfrac{{{\text{Total mass}}}}{{{\text{Molecular mass}}}}$ we can put this value in the gas equation and we get,
$PV = \dfrac{{Mass \times RT}}{M}$
3) Now that we know the density $\left( \rho \right) = \dfrac{{Mass}}{{Volume}}$ , by putting this value in the above equation we get,
$P = \dfrac{{\rho \times RT}}{M}$
4) As we got the density in the formula let's put aside the values and get the mathematical expression for density as follows,
$\rho = \dfrac{{M \times P}}{{RT}}$
5) Hence, we got the formula for density as $\rho = \dfrac{{M \times P}}{{RT}}$

So, the correct answer is Option B .

Note:
To solve this question one can relate the mathematical formulas given in options with respect to what has been asked. This will help for quickly solving the question. The density of the gas is equivalent to its mass partitioned by the volume. You can compute the molar mass of the substance once the density of the gas is known. The Density shifts with a change in temperature and weight.