D.

1/412

We know the molecular weight of C₈H₇SO₃Na
= 12x8+1x7+32+16x3+23 = 206
we have to find mole per gram of resin
therefore,
1 g of C₈H₇SO₃Na has number of mole

=1/206 mol
Taking the reaction,
C₈H₇SO₃Na + Ca²⁺ → (C₆H₇SO₃)2Ca + 2Na⁺
therefore, 2 moles of C₈H₇SO₃Na  combines with 1 mol of Ca²⁺
Thus, 1 mole of C₈H₇SO₃Na will combine with 0.5 mol of Ca²⁺
Hence, 1/206 mole of C₈H₇SO₃Na will combine with,
 0.5 x (1/206)mol of Ca²⁺ = 1/412 mol Ca²⁺

C.

-3.4 eV

Since at n=1 the population of electrons is maximum i.e. at the ground state. So, maximum excitation will take place from n = 1 to n=2.
Hence, n=2 is the possible excited state,
Now, we have the formula for energy of H-atom
(En)H = 
where Z = atomic number 
Z for H-atom = 1
therefore, (E_n)_H  = 

B.

ion-dipole interaction

 ion-ion interaction is dependent on the square of the distance,
i.e, ion-ion interaction ∝ 1/r²
Similarly, 
ion-dipole interaction ∝ 1/r³
London forces ∝ 1/r⁶
and dipole-dipole interactions ∝ 1/r³
superficially it seems as both ions interaction and hydrogen bonding vary with the inverse cube of the distance between the molecules but when we look at the exact expressions of field (force) created in two situations it comes as,
In the case of ion-dipole interaction:

and, In the case of dipole-dipole interaction

From the above it is very clear, the ion-dipole interaction is the better answer as compared dipole-dipole interaction i.e. hydrogen bonding.

D.

0.5[2 x 86600-R(298)In (1.6 x 10¹²)]

For the given reaction,
2NO(g) + O₂ (g) ⇌ 2NO₂ (g)
Given ,

Now, we have,

B.

reverse direction because Q>K_c

We know,
ΔG = ΔG^o + RTlnQ .. (i) 
Given,
ΔG^o  = 2494.2J
 
thus,
putting the value in equation (i)
 = 2494.2 +8.314 + 300 In 4
= 28747.27 J
= positive value
Also, we have

If ΔG is positive, Q >K
therefore, reaction shifts in the reverse direction