Answer

Verified

55.5k+ views

**Hint:**The graph is between pressure and density. To find the relation between the two masses can be obtained by using the expression for density and Boyle's law for an ideal gas. The density of a gas is the ratio of its mass to the volume. Boyle's law graphs are plotted with pressure on one axis and reciprocal of volume on the other axis. In this graph mass of the gas is multiplied by the volume to get density on the x-axis.

**Formula used:**

$d = \dfrac{m}{V}$ (Where d stands for the density, m stands for the given mass and V stands for the volume)

The ideal gas equation is given by,

$PV = nRT$ (where P is the pressure of the gas, V is the volume of the gas, n stands for the number of moles, R stands for the universal gas constant and T is the temperature of the gas)

**Complete step by step solution:**

We know that in the graph, pressure versus density is shown,

We know the expression for density,

Density $d = $$\dfrac{{mass}}{{volume}} = \dfrac{m}{V}$

Boyle's law for ideal gases is given by,

$PV = nRT$

$n$ is the number of moles which is given by, $\dfrac{{mass(given)}}{{Mass(molecular)}} = \dfrac{m}{M}$

where$ M$ is the molecular weight.

Substituting the value of $n$ in the ideal gas equation,

$PV = \dfrac{m}{M}RT$

Rearranging this equation, we get the density

Density, $(d)= \dfrac{m}{V} = \dfrac{{PM}}{{RT}}$

The graph of pressure versus density is shown in the figure as a straight line.

From the equation, we get that the slope of this line is, $\dfrac{{RT}}{M}$

As the molecular mass is in the denominator, the line with a greater slope will be having less molecular mass.

Since ${M_2}$ is steeper than ${M_1}$, ${M_1}$ will be greater than ${M_2}$.

**Hence, the answer is (A), ${M_1} > {M_2}$.**

**Note:**The slope will be more for a steeper line. Boyle’s law states that for a constant temperature the volume of a given mass of a gas is inversely proportional to volume. Gases are liquefied by using the principle of Boyle’s law. Boyle's law has many real-life applications also. The injection syringe is one example of Boyle's law.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

A convex lens is dipped in a liquid whose refractive class 12 physics JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

Water rises to height h in the capillary tube If the class 11 physics JEE_Main

The arrow in the symbol of a transistor indicates A class 12 physics JEE_Main

A train starts from rest from a station with acceleration class 11 physics JEE_Main