Question

What is the pH of a solution containing 10 g of HCOOH, formic acid dissolved in enough water to make 250 mL of solution?

Answer 1

Let a be the dissociation of the weak acid
                            HA <---> H ⁺ + A^-

initial conc.            c               0         0

change                -ca            +ca      +ca

Equb. conc.         c(1-a)          ca       ca

Dissociation constant , K_a = ca x ca / ( c(1-a)

                                         = c a² / (1-a)

In the case of weak acids α is very small so 1-a is taken as 1

So K_a = ca²

==> a = √ ( K_a / c )

Given K_a = 1.7 x10^-4

          c = concentration = (mass/molar mass) /volume of solution in L

                                     = ( 10 g / 46 (g/mol) )/ 0.250L

                                     = 0.869 M

Plug the values we get a =0.0139

[H⁺] = ca = 0.869 x 0.0139 = 0.01215 M

pH = - log [H⁺] = - log 0.01215

                       = 1.91