Which solution has higher conductivity: 4.5M HCN or 0.0010M HNO3.  Support your answer using calculations. What I have written down: HCN <--> H+ + CN- (All species have a molarity of 4.5 M)...

Which solution has higher conductivity: 4.5M HCN or 0.0010M HNO3.  Support your answer using calculations.

What I have written down:

HCN <--> H+ + CN- (All species have a molarity of 4.5 M)

HNO3 <--> H+ + NO3- (All species have a molarity of 0.0010 M)

Now what do I do?? Someone please explain this to me.

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llltkl | College Teacher | (Level 3) Valedictorian

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Conductivity in solution depends upon the number of ions present in a solution. Hydrgen cyanide, HCN is a weak acid with a very low acid dissociation constant (Ka=6.2×10˄-10). Considering its dissociation with degree of dissociation, α one can write

         HCN↔H+ + CN-

  c(1- α)       cα       cα

Ka = cα* cα/ c(1- α) = cα2 or, α = √(Ka/c)

And [H+]=[CN-] = cα = c√(Ka/c) = √(Ka*c)

Here Ka = Ka=6.2×10˄-10, c = 4.5

Putting these values, [H+]=[CN-]= √(6.2×10˄-10*4.5) = 5.3×10˄-5

In other words there will be 5.3×10˄-5 number of ions of each species in solution.

HNO3 is a strong electrolyte dissociating completely in solution. So for a 0.0010M solution of HNO3, [H+]=[NO3-]= 0.0010 = 1.0×10˄-3. This is much higher. Hence 0.0010M solution of HNO3 shall have higher conductivity.

Sources:

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