Charles' law states that for a fixed mass of a gas at constant pressure, the volume is directly proportional to temperature (K).
\(V\propto T\) (or)  = \(\frac{V}{T}\) Constant

Volume vs Temperature:
If a balloon is moved from an ice water bath to a boiling water bath, the gas molecules inside move faster due to increased temperature and hence the volume increases.

According to Boyle's law, at constant temperature for a given mass of gas at constant temperature,
P₁V_I = P₂V₂ = P₃V₃
1 atm x 1 dm³ = 2 atm x V₂ = P₃ x 0.25 dm³
\(\therefore\) 2 atm x V₂ = 1 atm x 1 dm³

\(\boxed{V_2=0.5\ dm^3}\)
and P₃ x 0.25 dm³ = 1 atm x 1 dm³

\(\boxed{P_3=4\ atm}\)

On heating incineration might take place due to the increase of pressure

a) Hydrogen is the lightest gas in the atmosphere. So it rises up and other gases which are heavier like O₂ & N₂ come down towards the surface of the earth according to Graham's law of diffusions \(\mathrm{r} \alpha \sqrt{\frac{1}{M}}\). Hydrogen diffuses very fast. Its mean speed in greater than the escape velocity from the earth. As a consequence, H₂ would have escaped from the atmosphere long time ago.
b) The acceleration due to gravity 'g' on moon surface is small. The value of escape velocity is also small. The molecules of the atmospheric gases on the moon's surface have thermal velocities greater than the escape velocity.
All the molecules have escaped. So the atmosphere is so thin.

This is due to the smaller size and relatively high charge as Be²⁺ ion. Moreover Beryllium is a non - metal. But Magnesium is a metal. In the case of beryllium the ionisation energy and electronegativity of the halides are almost similar; but there is a vast difference in IE and electronegativity between Mg and halides.

The largest use of plaster of paris is in the building industry as well as plasters. It is used for immobilising the affected part of organ where there is a bone fracture or sprain. It is also employed in dentistry, in ornamental work and for making casts of statues and busts.

Time taken for effusion of gas A = 73 seconds
Time taken for effusion of SO₂ gas = 75 seconds
Volume of gases (A & SO₂) taken = 75 ml each.
Molecular mass of SO₂ =
\(\frac { Effusion\ rate\ of\ { SO }_{ 2 } }{ Effusion\ rate\ of\ A } =\sqrt { \frac { { M }_{ A } }{ { M }_{ { SO }_{ 2 } } } } \)
\(\frac { 75/75 }{ 75/73 } =\sqrt { \frac { { M }_{ A } }{ { M }_{ { SO }_{ 2 } } } } ;\frac { 1 }{ 1.027 } =\sqrt { \frac { { M }_{ A } }{ 64 } } \)
\({ (0.9737) }^{ 2 }=\frac { { M }_{ A } }{ 64 } ;{ M }_{ A }=60.67\)
\(\therefore\)  Molecular mass of A is 60.67.

(i) Isotherm:
At any constant temperature when pressure is increased, volume is decreased and vice versa. Such P - V curves at constant temperature are known as isotherms.
(ii) Critical Temperature: (T_c)
It is defined as the characteristic temperature of a gas above which no liquefaction occurs.
(iii) Critical Pressure: (P_c)
It is defined as the minimum pressure required to liquefy 1 mole of a gas present at its critical temperature.
(iv) Critical volume: (V_c)
The volume occupied by 1 mole of a gas at its critical pressure and at critical temperature is the critical volume of the gas
(v) Compressibility factor:
The deviation of real gases from ideal behaviour is measured in terms of a ratio of PV to nRT. This is termed as compressibility factor.
\(Z=\frac { PV }{ nRT } \)

(i) Alkaline earth metal (A) belonging to 3rd period is magnesium.
(ii) So A is Magnesium. Magnesium reacts with oxygen and nitrogen as follows.
\(2Mg+O_2⟶\underset{(B)}{2MgO}\)
\(3Mg+N_2⟶\underset{(C)}{Mg_3N_2}\)
So B is Magnesium oxide and C is magnesium nitride.
(iii) Magnesium undergoes metal displacement reaction with AgNO₃ as follow to give D as follows :
\(Mg+2AgNO_3⟶\underset{D}{Mg(NO_3)_2}+2Ag\)
So D is Magnesium nitrate.
Result  :

Magnesium oxide in having higher melting point. The lattice energy of MgO & MgF₂ are 3938 and 2957 respectively.
MgO has +2, -2 charges, MgF₂ has +2, -1 charges. When the two charges are multiplied together, MgO results in larger amount of lattice energy since it has a higher charge, The strong attraction cause most ionic material to be hard and brittle and have high melting points.

(i) Sodium hydroxide is used as laboratory reagent.
(ii) It is used in the purification of bauxite and petroleum refining.
(iii) It is used in the textile industries for mercerising cotton fabrics.
(iv) It is used in the manufacture of soap, paper, artificial silk and a number of chemicals.

The solubility product of NaCl is lower than that of NaOH. The more soluble a substance is, the higher the K_sp value it has In aqueous solution NaOH gives OH^- ions. It can be solvated by establishing H-bonds with water molecules. So it is more water soluble.