The modem periodic law states that, "the physical and chemical properties of the elements are periodic functions of their atomic numbers."

The first law of thermodynamics, also known as the law of conservation of energy, states that "The total energy of an isolated system remains constant though it may change from one form to another."
The mathematical statement of the First Law is: ΔU=q+w
Where q - the amount of heat supplied to the system; w - work done on the system

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.

a) Electron-precise hydrides:
These have required number of electron to represent their conventional d lewis structure. All the elements of carbon group (14) form such hydrides.
Eg CH₄, C₂H₆, SiH₄, GeH₄
b) Electron - deficient hydrides:
There act as Lewis acids (ie) electron acceptors. The elements from group (13) form such hydrides.
Eg: B₂H₆
c) Electron - rich hydrides:
There have excess electron, which are present as lone pairs. Elements of group 15-17 form such hydrides. They behave as Lewis bases (ie) electron donors.
Eg: NH₃ ,H₂O, HF

(i) State function: A state function is a thermodynamic property of a system, which has a specific value for a given state and does not depend on the path (or manner) by which the particular state is reached.
Example: Pressure (P), Volume (V), Temperature(T)
(ii) Path functions: A path function is a thermodynamic property of the system whose value depends on the path by which the system changes from its initial to final states.
Example: Work (w), Heat (q).

The balanced equation for the combustion of ethane
C₂H₆ + \(\frac { 7 }{ 2 } \)O₂ \(\longrightarrow \) 2CO₂ +3H₂O
2C₂H₆ + 7O₂ \(\longrightarrow \) 4CO₂ + 6H₂O
To produce 4 moles of CO₂, 2 moles of ethane is required
To produce 1 moles (44 g) of CO₂ required
Number of moles of ethane
\(=\frac{2 \mathrm{~mol} \text { ethane }}{4 \not \mathrm{molCO}_{2}} \times 1 \not \mathrm{molCO}_{2}\)
= \(\frac { 1 }{ 2 } mole\quad of\quad ethane\)
= 0.5 mole of ethane

Calcium Sulphate (plaster of paris), CaSO₄. 1/2H₂O :
It is a hemihydrate of calcium sulphate. It is obtained when gypsum, CaSO₄ .2H₂O,is heated to 393 K
2(CaSO₄.2H₂O) ⟶ 2CaSO₄,H₂O + 3H₂O
Above 393 K, no water of crystallisation is left and anhydrous calcium sulphate, CaSO₄ is formed. This is a known 'dead burnt plaster'.
It has a remarkable property of setting with water. on mixing with an adequate quantity of water it forms a plastic mass that gets into hard solid in 5 to 15 minutes.

1. Heavy water is widely used as moderator in nuclear reactors as it can lower the energies of fast neutrons
2. It is commonly used as a tracer to study organic reaction mechanisms and mechanism of metabolic reactions
3. It is also used as a coolant in nuclear reactors as it absorbs the heat generated.

(i) Lithium and beryllium form more covalent compounds, unlike the alkali and alkali earth metals which predominantly form ionic compounds.
(ii) The elements of the second period have only four orbitals (2s & 2p) in the valence shell and have a maximum co-valence of 4, whereas the other members of the subsequent periods have more orbitals in their valence shell and shows higher valences. For example, boron forms BF₄^- and aluminium forms AIF₆^3-.

ΔH_c(CH₄)= - 890 kJ mol^-1
ΔH_c(C₂H₄) = -1423 kJ mol^-1
ΔH_c=-203.87 kJ mol^-1
Let the mixture contain x lit of CH₄ and (3.67 - x)
lit of ethylene
CH₄+2O₂\(\rightarrow \)2CO₂+2H₂O
XLit
C₂H₄+3O₂\(\rightarrow \)2CO₂+2H₂O
(3.67-X)Lit       2(3.67-X)Lit
Volume of Carbondioxide formed
=x + 2 (3.67 - x) = 6.11 lit
X+7.34-2X=6.11
7.34-X=6.11
X=1.23Lit
Given mixture contains 1.23 lit of methane and 2.44 lit of ethylene, hence
\(\triangle { H }_{ C }=\left[ \frac { \triangle { H }_{ C }\left( { CH }_{ 4 } \right) }{ 22.4Lit } \times \left( X \right) lit \right] +\left[ \frac { \triangle { H }_{ C }\left( { C }_{ 2 }{ H }_{ 4 } \right) }{ 22.4lit } \times \left( 3.67-X \right) lit \right] \)
\(\triangle { H }_{ C }=\left[ \frac { -890KJ{ mol }^{ -1 } }{ 22.4Lit } \times 1.23lit \right] +\left[ \frac { -1423 }{ 22.4lit } \times \left( 3.67-1.23 \right) lit \right] \)
ΔH_c =[-48.87kJ mol^-1]+[-155kJ mol^-1]
ΔH_c =-203.87kJ mol^-1 .

Characteristics of internal energy (U) :

• The internal energy of a system is an extensive property.
• The internal energy of a system is a state function.
• The change in internal energy of a system is expressed as ΔU= U_f - U_i
• In a cyclic process,' there is no internal energy change. ΔU_(cyclic)= 0
• If the internal energy of the system in the final state (U_f) is less than the internal energy of the system in its initial state (U_i), then ΔU would be negative.
• ΔU = U_f- Ui = -ve (U_f < U_i)
• If the internal energy of the system in the final state (U_f) is greater than the internal energy of the system in its initial state (U_i), then ΔU would be positive.
• ΔU = U_f - U_i = +ve (U_f > U_i)

2Al + Fe₂O₃ \(\longrightarrow \)  Al₂O₃ + 2Fe

Molar mass of Al₂O₃ format = 6 mol x 102 g mol^-1 = 612 g
[  Al₂O₃ : (2 x 27) + 3(16) = 54 + 48 = 102] = 612 g
Excess reagent = Fe₂O₃
Amount of excess reagent left at the end of the reaction = 1 mol x 160 g mol^-1
= 160g [ Fe₂O₃ : (2 x 56) + (3 x 16) = 112 + 48 = 160] = 160 g

The word Aufbau in German means 'building up'. In the ground state of the atoms, the orbitals are filled in the order of their increasing energies. That is the electrons first occupy the lowest energy orbital available to them.
Once the lower energy orbitals are completely filled, then the electrons enter the next higher energy orbitals. The order of filling of various orbitals as per the Aufbau principle which is in accordance with (n + l) rule.

On moving diagonally across the periodic table, the second and third period elements show certain similarities. It is quite pronounced in the following pair of elements.

The similarity in properties existing between the diagonally placed elements is called diagonal relationship.