# NCERT Class 11 Physics Solutions: Chapter 13 – Kinetic Theory-Part 1

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**Question 13.1:**

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at . Take the diameter of an oxygen molecule to be

**Answer:**

Diameter of an oxygen molecule,

Radius,

Actual volume occupied by 1 mole of oxygen gas at

Molecular volume of oxygen gas,

Where, is Avogadro’s number molecules/mole

Ratio of the molecular volume to the actual volume of oxygen

**Question 13.2:**

Molar volume is the volume occupied by of any (ideal) gas at standard temperature and pressure ( atmospheric pressure, 0 °C). Show that it is 22.4 litres.

**Answer:**

The ideal gas equation relating pressure volume and absolute temperature is given as:

Where,

s the universal gas constant

Number of moles

Standard temperature

Standard pressure

Hence, the molar volume of a gas

**Question 13.3:**

Figure shows plot of versus for of oxygen gas at two different temperatures

What does the dotted plot signify?

Which is true:

What is the value of where the curves meet on the y-axis?

What is the value of where the curves meet on the y-axis?

If we obtained similar plots for of hydrogen, would we get the same value of at the point where the curves meet on the ? If not, what mass of hydrogen yields the same value of (for low pressure high temperature region of the plot)? (Molecular mass of

**Answer:**

The dotted plot in the graph signifies the ideal behaviour of the gas, i.e., the ratio is equal is the number of moles and R is the universal gas constant) is a constant quality. It is not dependent on the pressure of the gas.

The dotted plot in the given graph represents an ideal gas. The curve of the gas at temperature is closer to the dotted plot than the curve of the gas at temperature. A real gas approaches the behaviour of an ideal gas when its temperature increases. Therefore, is true for the given plot.

The value of the ratio , where the two curves meet, is This is because the ideal gas equation is given as:

Where,

is the pressure

is the temperature

is the volume

is the number of moles

is the universal constant

Molecular mass of oxygen

Mass of oxygen

Therefore, the value of the ratio where the curves meet on the , is

If we obtain similar plots for of hydrogen, then we will not get the same value of at the point where the curves meet the . This is because the molecular mass of hydrogen (is different from that of oxygen

We have:

Molecular mass

at constant temperature

Where,

Mass of

Hence of will yield the same value of