Is the density of an ideal gas at constant pressure inversely proportional to the temperature?

At a constant pressure, the density of a certain amount of an ideal gas is ____________.

directly proportional to the temperature
inversely proportional to the temperature
directly proportional to the square of the temperature
independent of a temperature

At a constant pressure, the density of a certain amount of an ideal gas is inversely proportional to the temperature.

Explanation:

The density of an ideal gas is given as

d = `"PM"/"RT"`

∴ `"d" ∝ 1/"T"` ......(∵ P, M, R = constant)

Concept: Ideal Gas Equation

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Answer

Verified

Hint:To find the relation between density, pressure and temperature, try to think logically what will happen to the density when pressure or temperature will increase.The ideal gas law, also known as the general gas equation is an equation of state of a hypothetical ideal gas. Although the ideal gas law has several limitations, it is a good approximation of the behaviour of many gases under many conditions.

Complete step by step answer:

Density is the measure of the mass of an object per unit volume. It is denoted as \['\rho '\].\[\rho =\dfrac{M}{V}\] Where \[\rho \] is the density, \[M\] is the mass in kgs and \[V\] is the volume in \[{{m}^{3}}\]. Therefore, the SI unit of density is \[kg/{{m}^{3}}\]. Density describes how closely packed the particles are in a solid,liquid or gas. So, if we increase the temperature of any substance, its particles will start vibrating with more kinetic energy and as a result intermolecular space increases, which means its volume will increase. Hence, the density will decrease as density is mass per unit volume.When we increase the pressure, keeping the temperature constant, the intermolecular space between the particles decreases and hence the same mass gets concentrated in a much smaller volume which means the density will increase. Hence, the density is directly proportional to the pressure. If you don’t want to think it logically, there is a very popular equation which is derived from ideal gas equation\[Density=\dfrac{PM}{RT}\] Where $P$ = Pressure, $M$ \[=\] Molar mass of the gas, $R$ = Universal Gas constant and $T$ = Temperature. Clearly, we can see it is directly proportional to its pressure and inversely proportional to its absolute temperature.

Hence, the correct answer is option B.

Note:This is generally the case that as temperature increases density decreases but there is one exception to this which is water. When the temperature of water is decreased, its density increases(the water contracts) but this behaviour is upto \[{{4}^{\circ }}\] celsius only. After \[{{4}^{\circ }}\] celsius, if we further decrease the temperature, its density decreases(the water expands) and this behaviour of water is called anomalous expansion of water.