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.
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.