ΔH_f(Fe₂O₃)= -741 kJ mol^-1
ΔH_f(CO)= -137 kJ mol^-1
ΔH_f(CO₂)= -394.5 kJ mol^-1
Fe₂O₃ + 3CO ⟶ 2Fe + 3CO₂ ΔH_r=?
ΔH_r=Σ(ΔH_f)products - Σ(ΔH_f)reactants
ΔH_r=[2ΔH_f=(Fe)+3ΔH_f(CO₂)]-[ΔH_f(Fe₂O₃)+3ΔH_f(CO)]
ΔH_r=[0 + 3 (-394.5)] - [-741 +3 (-137)]
ΔH_r=[-1183.5] - [-1152]
ΔH_r=-1183.5 + 1152
ΔH_r=-31.5 kJ 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

Screening effect: The repulsive force between the inner shell electrons and the valence electrons leads to a decrease in the electrostatic attractive forces acting on the valence electrons by the nucleus. Thus, the inner shell electrons act as a shield between the nucleus and the valence electrons. This effect is called shielding effect.
Pauling's scale: Pauling, he assigned arbitrary value of electronegativities for hydrogen and fluorine as 2.2 and 4.0 respectively. Based on this the electronegativity values for other elements can be calculated using the following expression.
\(({ X }_{ A }-{ X }_{ B })=0.182\sqrt { E_{ AB } } -({ E }_{ AA }*{ E }_{ BB })^{ 1/2 }\)
Where E_AB' EAA and E_BB are the bond dissociation energies of AB, A₂ and B₂ molecules respectively. The electronegativity of any given element is not a constant and its value depends on the element to which it is covalently bound. The electronegativity values play an important role in predicting the nature of the bond.

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.

\(\triangle\)x = 0.6\(\mathring{A}\) = 0.6 x 10^-10m
\(\triangle p\) = ?
\(\triangle x.\triangle p\ge\frac{h}{4\pi}\)
\(\triangle x.\triangle p\ge5.28\times10^{-35}kgm^{2}s^{-1}\)
\((0.6 \times10^{-10}) \triangle p \ge5.28\times10^{-35}\)
\(\Rightarrow \triangle \ge \frac{5.28\times10^{-35}kgm^{2}s^{-1}}{0.6510^{-1}m}\)
\(\triangle p \ge8.8\times10^{-25}kgms^{-1}\)

\({ He }^{ + }\longrightarrow { He }^{ 2+ }+{ e }^{ - }\)
\({ E }_{ n }=\frac{-13.6(2)^2}{n^2}\)
\({ E }_{ 1 }=\frac{-13.6(2)^2}{(1)^2}=-54.4\)
\({ E }_{ \infty }=\frac{-13.6(2)^2}{(\infty)^2}=0\)
\(\therefore\) Required Energy for the given process
= E_\(\infty\) - E_I = 0 - (- 54.4) = 56.4 ev.

High purity hydrogen (> 99.9%) is obtained by the electrolysis of water containing traces of acid or alkali or the electrolysis of aqueous solution of sodium hydroxide or potassium hydroxide using a nickel anode and iron cathode. However, this process is not economical for large-scale production.
 At anode: 2OH^- ➝ H₂O + 1/2O₂ + 2e^-
At cathode: 2H₂O + 2e^- ➝ 2OH^- + H₂
Overall reaction: H₂O ➝ H₂ + 1/2O₂ 

1. Gypsum is used in making drywalls or plaster boards.
2. Another important use of gypsum is the production of plaster of Paris. Gypsum is heated to about 300 degree Fahrenheit to produce plaster of paris, which is also known as gypsum plaster. It is mainly used as a sculpting material.
3. Gypsum is used in making surgical and orthopedic casts, such as surgical splints and casting moulds.
4. Gypsum plays an important role in agriculture as a soil additive, conditioner, and fertilizer. It helps loosen up compact or clay soil, and provides calcium and sulphur, which are essential for the healthy growth of a plant.
5. Gypsum is used in toothpastes, shampoos, and hair products.
6. Gypsum is a component of portland cement, where it acts as a hardening retarder to control the speed at which concrete sets.