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The molality of (NH4)2SO4 solution that has the same ionic strength as 1 mol kg–1 solution of KCl is:
  • a)
    1/3 mol kg–1
  • b)
    1/2 mol kg–1
  • c)
    2/5 mol kg–1
  • d)
    3/5 mol kg–1
Correct answer is option 'A'. Can you explain this answer?
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The molality of (NH4)2SO4 solution that has the same ionic strength as...
Calculation of Ionic Strength:

Ionic strength is the measure of the concentration of ions in a solution. It is calculated using the formula:

Ionic strength (I) = 1/2 ∑ ci zi^2

Where,
ci = concentration of the ith ion
zi = charge on the ith ion

For 1 mol kg^-1 solution of KCl, the concentration of K+ and Cl- ions is 1 mol kg^-1 each. Therefore,

Ionic strength (I) = 1/2 [ (1 mol kg^-1) (1^2) + (1 mol kg^-1) (1^2) ]
I = 1 mol kg^-1

Calculation of Molality of (NH4)2SO4 solution:

To find the molality of (NH4)2SO4 solution that has the same ionic strength as 1 mol kg^-1 solution of KCl, we need to first calculate the concentration of ammonium and sulfate ions in the solution.

(NH4)2SO4 dissociates to give 2 NH4+ ions and 1 SO4^2- ion. Therefore, the total concentration of ions in the solution is:

Concentration of ions = 2[NH4+] + [SO4^2-]

Let x be the molality of (NH4)2SO4 solution. Then,

Concentration of NH4+ ions = 2x mol kg^-1
Concentration of SO4^2- ion = x mol kg^-1

Using the formula for ionic strength, we can write:

I = 1/2 [ (2x mol kg^-1) (1^2) + (x mol kg^-1) (2^2) ]
1 = 2x + 2x
x = 1/3 mol kg^-1

Therefore, the molality of (NH4)2SO4 solution that has the same ionic strength as 1 mol kg^-1 solution of KCl is 1/3 mol kg^-1.
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