(i) Over a range of low pressures, the real gases can behave ideally at a particular temperature called as Boyle temperature or Boyle point.
(ii) The Boyle point varies with the nature of the gas.
(iii) Above the Boyle point, the compression point Z > 1 for real gases i.e. real gases show positive deviation.
(iv) Below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increase with increase in pressure. So, it is clear that at low pressure and at high temperature, the real gases behave as ideal gases.
(v) Hence, \(Z=\frac{PV_{real}}{nRT}\)
\(PV_{ideal}=\frac{nRT}{P}\)
So, \(Z=\frac{V_{real}}{V_{ideal}}\)

(i) Variation of volume of the gas sample with temperature at constant
(ii) Each line (iso bar) represents the variation of volume with temperature at certain pressure. The pressure increases from P₁ to P₅.
(iii) i.e. P₁ < P₂ < P₃ < P₄ < P₅ When these lines are extrapolated to zero volume, they intersect at a temperature of -273.15°C.
(iv) All gases are becoming liquids if they are cooled to sufficiently low temperatures.
(v) In other words, all gases occupy zero volume at absolute zero. So the volume of a gas can be measured over only a limited temperature range.

According to Charles' law,
\(\frac{V_1}{T_1}=\frac{V_2}{T_2}=\frac{V_3}{T_3}\)
\(\frac{0.3dm^3}{200K}=\frac{V_2}{300K}=\frac{0.15dm^3}{T_3}\)
\(\frac{V_2}{300K}=\frac{0.3dm^3}{200K}\)

V₂ = 0.45 dm³ and
\(\frac{0.15dm^3}{T_3}=\frac{0.3dm_3}{200K}\)

T₃ = 100 K.

According to Boyle 's law for a given mass of a gas under two different sets of conditions at constant temperature we can write
P₁V₁ = P₂V₂ = k           . ...(1)

V₁ = 0.375 dm³ V₂ = 0.125
P₁ = 1.05 atm  P₂ = ?
' T '- Constant
P₁V₁  = P₂V₂
\(\therefore \) P₂  = \(\frac { { P }_{ 1 }{ V }_{ 1 } }{ { V }_{ 2 } } =\frac { 1.05\times 0.375 }{ 0.125 } \)  = 3.15 atm

The larger the size of the molecule, the greater will be Van der Waals' attraction. Therefore greater the deviation from ideal behaviour. So bromine will deviate more from ideal behaviour because it has bigger atoms.

If there is a tiny sticky area on the walls of the container of a gas, then the collision of the molecules will not be elastic. So the gas will behave as a real gas. So the pressure will be less than the calculated value.

It is defined as the number of molecules of a gas that get diffused in unit time.
rate of diffusion = \(\frac{Volume\ of \ the\ gas\ diffused}{time\ taken}\)

(i) The individual gas molecules occupy negligible volume when compared to the total volume of the gas.
(ii) There is no attractive force between the gas molecules.

The pressure decreases with the increase in altitude because there are fewer molecules per unit volume of air. Above 9200 m (30000 ft.) the pressure is so low that one could pass out for lack of oxygen. For this reason most airplanes cabins are artificially pressurized.

The gas deviates from ideal gas behaviour and will be a real gas only. In the compressed state, the inter molecular forces will be very high as the molecules are very close.

P_total = X_i - P_total
Assuming that the gases behave ideally,
\(p_1=n_1{{RT}\over{V}};p_2=n_2{{RT}\over{V}};p_3=n_3{{RT}\over{V}}\)
\(\mathrm{p}_{\text {Total }}=\mathrm{n}_{1} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{2} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{3} \frac{\mathrm{RT}}{\mathrm{V}}=\left(\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}\right) \frac{\mathrm{RT}}{\mathrm{V}}\)
\(\mathrm{P}_{\text {Total }}=\mathrm{n}_{\text {Total }}\left(\frac{\mathrm{RT}}{\mathrm{V}}\right)\)
The partial pressure can also be expressed as
\(\left( {{RT}\over{V}} \right)\) can be expressed as \({{p_1}\over{n_1}}\) or \({{p_2}\over{n_2}}\) or \({{p_3}\over{n_3}}\) or in general in \({{p_i}\over{n_i}}\)
Therefore
\( \mathrm{p}_{\text {Total }} =\mathrm{n}_{\text {Total }} \frac{\mathrm{p}_{\mathrm{i}}}{\mathrm{n}_{\mathrm{i}}}=\frac{\mathrm{n}_{\text {Total }}}{\mathrm{n}_{\mathrm{i}}} \mathrm{p}_{\mathrm{i}} \)
\(\Rightarrow \mathrm{p}_{\mathrm{i}} =\frac{\mathrm{n}_{\mathrm{i}}}{\mathrm{n}_{\text {Total }}} \mathrm{p}_{\text {Total }}=x_{\mathrm{i}} \mathrm{p}_{\text {Total }}\)
where x_i is the mole fraction of the i^th component.

Astronauts must wear space suits filled with air, whenever they leave a space craft and are exposed to the environment of space.
Dangers experienced on moon's space :
1. In space there is no air to breathe and no air pressure.
2. Space is extremely cold and filled with dangerous radiations.
3. If they do not wear space suits, there may be bleeding due to high body pressure.
4. The space suits prevent astronauts from impacts of small bits of space dust.
5. There is no atmosphere on the moon and there are dangers from micro-meteorite impacts.
6. The astronauts are protected from these dangers on wearing space suits.