What multiple of Ka must the initial concentration of a weak acid exceed, for the initial concentration and the equilibrium concentration to be within 9.40 percent of each other?  

In an aqueous solution of a weak acid, HA, the assumption is often made that [HA] equilibrium = [HA]initial. This approximation is reasonable if the initial concentration of the acid is sufficiently large compared to Ka. What multiple of Ka must the initial concentration of a weak acid exceed, for the initial concentration and the equilibrium concentration to be within 9.40 percent of each other?

 

Solution

Let initial concentration [HA]o = x M

 The equilibrium concentration =[HA] = (100 – 9.40)/100 * xM

= 0.906xM

The change in concentration [HA]o – [HA] = x M – 0.906xM = 0.094xM = [A-] = [H+]

The equilibrium constant Ka = [H+] [A-] /HA = 0.094x * 0.094x / 0.906x = 0.00975x

Hence, the initial concentration of a weak acid is x/Ka = x /0.00975x =102.56 =10

Hence, multiple of Ka must the initial concentration of a weak acid exceed, for the initial concentration and the equilibrium concentration to be within 9.40 percent of each other will be = 103 – 1 = 102 multiple of Ka (1 subtracted because of round off above)

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