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(a) Since Ka1 >> Ka2, you can ignore the second ionization. However, you\\\'ll n

ID: 889299 • Letter: #

Question

(a) Since Ka1 >> Ka2, you can ignore the second ionization. However, you'll need to use either the quadratic equation or successive approximations to solve for [H ].

(b) 25.0 mL is half way to the first equivalence point, so pH = pKa1.

(c) 50.0 mL is the first equivalence point. H2PO3– is amphoteric, so use pH = 1/2(pKa1 pKa2).

(d) 75.0 mL is half way to the second equivalence point, so pH = pKa2.

(e) 100.0 mL is the second equivalence point. The final product, HPO32–, is a weak base with Kb1 = Kw/Ka2.

Explanation / Answer

Solution :-

a) Calculating pH before adding any KOH

Pka 1 = 1.30

Therefore Ka1 = Anitlog[-1.30] = 5.01*10^-2

Using the ka1 lets calculate the pH

H3PO3 + H2O ----- >   H3O+ + H2PO3^-

3.0 M                              0              0

-x                                    +x           +x

3.0-x                             x              x

Ka1 = [H3O+] [H2PO3-]/[H3PO3]

5.01*10^-2 = [x][x]/[3.0-x]

5.01*10^-2 * 3.0-x = x^2

By solving this using the quadratic equation we get

X= 0.3634 M

Therefore pH is

pH= -log [H3O+]

pH = - log [0.3634]

pH= 0.440

b) calculating pH after adding 25 ml of 3.0 M KOH

molarity of the Acid is 3.0 M

therefore it reaches the half way of the first equivalence point

where moles of the acid and the moles of the conjugate base are same

therefore

pH= pka1

pH= 1.30

c) Calculating pH after adding 50 ml of 3.0 M KOH

At this addition titration reaches to the first eqeuivalence point means all the acid H3PO3 is converted to the H2PO3-

Therefore

pH = ½ (pka 1 + pka2)

pH = ½ (1.30+6.70)

pH= 4

d) Calculating pH after adding 75 ml of 3.0 M KOH

Here titration reaches to the half way of the second equivalence point means

Half of HPO3^- changes to PO3^2-

Therefore

pH = pka2

pH= 6.70

e) Calculating pH after adding 100 ml of 3.0 M KOH

At this point all the HPO3- changes to the PO3^2-

Therefore

Concentration of the PO3^2- is halved because the volume is doubled (100 ml + 100 ml =200 ml )

Therefore new concentration of the PO3^2- = 3.0 M / 2 = 1.5 M

Kb1= Kw / ka2

Kb1 = 1*10^-14 / 5.01*10^-2

Kb1 = 2.0*10^-13

Therefore using the Kb1 lets calculate the OH^-

PO3^2- + H2O -------- > HPO3^- + OH^-

1.5 M                                     0             0

-x                                            +x           +x

1.5-x                                        x            x

Kb1 = [HPO3^-][OH-]/[PO3^2-]

2.0*10^-13 = [x][x]/[1.5-x]

Sinc kb1 is very small therefore neglect the x from the denominator

Therefore

2.0*10^-13 = x^2 / 1.5

2.0*10^-13 * 1.5 = x^2

3*10^-13 =x^2

Taking square root of both sides we get

5.477*10^-7 = x = [OH-]

Now lets find the pOH

pOH= -log [OH-]

pOH= -log[5.477*10^-7]

pOH = 6.26

now lets find the pH

pH= 14 – pOH

pH= 14 – 6.26

pH= 7.74