A disproportionation reaction is a type of redox reaction where a single substance undergoes both oxidation and reduction, forming two different products.

Let's analyze each option:

(a) 2 F_2(g) + 2 OH^-_(aq) → 2 F^-_(aq) + OF_2(g) + H₂O(l)

• This reaction involves fluorine (F₂), which is reduced to F^- and oxidized to OF₂. Therefore, fluorine undergoes both oxidation and reduction.
• This is a disproportionation reaction.

(b) Cl_2(g) + 2 OH^-_(aq) → ClO^-_(aq) + Cl^-(aq) + H₂O(l)

• In this reaction, chlorine (Cl₂) is reduced to Cl^- and oxidized to ClO^-.
• This is a disproportionation reaction.

(c) 2 NO_2(g) + 2 OH^-_(aq)→ NO₃^-_(aq) + NO₂^-_(aq) + H₂O(l)

• In this reaction, NO₂ undergoes both oxidation and reduction to form NO₃^- and NO₂^-.
• This is a disproportionation reaction.

(d) 2 H₂O_2(aq)→ 2 H₂O(l) + O_2(g)

In this reaction, hydrogen peroxide (H₂O₂) decomposes into water (H₂O) and oxygen (O₂). Here, hydrogen peroxide undergoes reduction to form H₂O and oxidation to form O₂, but since it does not involve two different products from a single reactant, it is not a disproportionation reaction. It's a simple decomposition reaction.

Conclusion:The reaction in (a) is the disproportionation reaction, so the correct answer is (d) 2 H₂O_2(aq) → 2 H₂O(l) + O_2(g).

For all spontaneous chemical reactions, the change in Gibbs free energy (ΔG°) is always negative.

For a spontaneous reaction in an electrolytic cell, the cell potential (E°cell) should be positive.

The correct answer is Option D.

The molar conductivity increases with decrease in concentration both, for weak and strong electrolytes.

This is because the total volume, V, of a solution containing one mole of electrolyte also increases. It has been found that a decrease in k on dilution of a solution is more than compensated by an increase in its volume.

Correct answer: C

Degree of dissociation (α) is given by α = Λ_c / Λ_∞.

α = 0.005 / 0.05 = 0.1

For the weak acid HA, at equilibrium [H⁺] = αc, [A^-] = αc and [HA] = c(1 - α). Hence

K_a = (α^2 · c) / (1 - α)

Calculate the numerator: α^2 · c = (0.1)^2 × 0.009 = 9×10^-5

Now divide by (1 - α) = 0.9 to get

K_a = (9×10^-5)/(0.9) = 1.0×10^-4

Therefore, K_a = 1.0×10^-4, so option C is correct.

Primary batteries cannot be recharged and reused.

Molar mass of CH₃COOH=60gmol^-1

Molar mass of C₂H₅OH=46gmol^-1

Molar mass of CH₃COOC₂H₅=88gmol^-1

∴[CH₃COOH)Initial=6060×5=0.2molL^-1

 [C₂H₅OH]Initial=4646×5=0.2molL^-1

[CH₃COOC₂H₅]eqm=4488×15=0.1molL-1

CH₃COOH+C₂H₅OH⇔CH₃COOC₂H₅+H₂O

Initial

0.2M          0.2M

0.2M           0.2M

At eqm.

(0.2−0.1)M (0.2−0.1)M 0.1M 0.1M

(0.2-0.1)M (0.2-0.1)M 0.1M 0.1M

∴K=[CH₃COOC₂H₅][H₂O]/[CH₃COOH][C₂H₅OH]

=0.1×0.1/0.1×0.1=1

In second case,

[CH₃COOH]Initial=0.4M

[C₂H₅OH]Initial=0.2M

If x is the amount of acid and alcohol reacted

[CH₃COOH]eqm.=(0.40-x)M

[C2H₅OH]eqm.=[0.2-x]M

[CH₃COOC₂H₅]eqm.=[H₂O]eqm.=xM

∴K=x²/(0.4-x)(0.2-x)=1

x=860M

∴Moles of ethyl acetate produced =860×5=23

Mass of ethyl acetate produced =23×88=58=58.66g.

ClO₃^- : A very reactive inorganic anion.

The term chlorate can also be used to describe any compound containing the chlorate ion, normally chlorate salts. 

Example: Potassium chlorate, KClO₃

Acid ⇋ Conjugate Base  +  H⁺

By this definition,

HNO2 ⇋ NO₂^- + H⁺

CH₃NH₃+ ⇋ CH₃NH₂ + H⁺

C₆H₅COOH ⇋ C₆H₅COO^- + H⁺

H₃O⁺ ⇋ H₂O + H⁺

We can see that the conjugate base of H₃O+ is H₂O. But it is given that OH^- is the C.B. So option d is incorrect.

For the buffer solution containing equal concentration of B^– and HB

pH = pK_a + log 1

pH = pK_a = 4

The octahedral complex ion [ CoCl₂(NH₃)₄]⁺ i.e., tetra amminedichloro cobalt (III) ion exists as cis and trans isomers.

In an electrochemical cell, when an opposing externally potential is applied and increased slowly, the reaction continues to take place.

When the external potential is equal to the potential of the cell, the reaction stops.

Once the externally applied potential is greater than the potential of the cell, the reaction goes in the opposite direction and the cell behaves like an electrolytic cell.