Question

Use the 5% rule to determine whether or not the equilibrium concentration of the acid can be approximated by its makeup concentration.

(a) 0.45 M cyanic acid (HCNO, pK_a = 3.46)
%

The approximation is valid.The approximation is not valid.    

(b) 0.0077 M hydrazoic acid (HN₃, pK_a = 4.6)
%

The approximation is valid.The approximation is not valid.    

(c) 1.5 M arsenic acid (H₃AsO₄, pK_a = 2.26)
%

The approximation is valid.The approximation is not valid.  

Answer 1

(a). [Acid] = 0.45M

pKa = 3.46

Ka = 10^-pKa

Ka = 10^-3.46

Ka = 3.4610^-4

Let the concentration of H⁺ ions is x

So, x = (Ka*[Acid]

x = (3.4610^-4*0.45)

x = 0.012

Now,

x/[acid]*100 = 0.012/0.45*100

= 2.66%

As this value is less than 5%, hence approximation is valid.

(b). [acid] = 0.0077M

pKa = 4.6

Ka = 10^-4.6

Ka = 2.5110^-5

x= ( 2.5110^-5*0.0077)

= 4.39X10^-4

x/[acid]*100 = 4.39X10^-4/ .0077*100

= 5.7%

As this value is greater than 5%, hence approximation is not valid.

(c). [acid] = 1.5M

pKa = 2.26

Ka = 10^-2.26

Ka = 5.49X10^-3

x = (5.49X10^-3*1.5)

= 0.090

x/[acid]*100 = 0.090/1.5*100

= 6%

As this value is greater than 5%, hence approximation is not valid.