Question

Sulfur dioxide is quite soluble in water: SO2(g)+H2O(l)⇌H2SO3(aq)K=1.33 The H2SO3 produced is a weak diprotic acid (Ka1 = 1.5×10−2, Ka2 = 6.3×10−8)

Part A Calculate the pH in a solution prepared by continuously bubbling SO2 at a pressure of 1.00 atm into pure water. Express your answer using two decimal places.

Part B Calculate the concentration of H2SO3. Express your answer using three significant figures.

Part C Calculate the concentration of HSO3−. Express your answer using two significant figures.

Part D Calculate the concentration of SO32−. Express your answer using two significant figures.

Answer 1

Given that for the equilibrium -

SO2(g) + H2O(l) <-> H2SO3(aq) K = 1.33

So, K = [H2SO3]/[pSO2] where [H2SO3] is the concentration of H2SO3 and pSO2 is the pressure of SO2 gas

so, at 1 atm pressure we have K = [H2SO3]/[1] = 1.33

so, [H2SO3] = 1.33 M

H2SO3 is a weak acid as its Ka values are small.

for a weak acid HA we have pH = -log([HA][Ka]) = -log(1.33*1.5*10^-2) = 1.7 (Assuming H+ ion coming from second dissociation of H2SO3 is negligible because its Ka2 value is also negligible)

As pH = 1.7 , [H+] = 10^-pH = 10^-1.7 = 0.02

H2SO3 dissociates as -

H2SO3 -> H+ + HSO3-

For this we have Ka1 = [H+][HSO3-]/[H2SO3] = 1.5*10^-2

Making ICE table we have -

H2SO3 -> H+ + HSO3-

I 1.33 0 0

C -1.33x +1.33x+1.33xy +1.33x - 1.33xy

E 1.33-1.33x 1.33x+1.33xy 1.33x-1.33xy

Putting the values we get 0.02*[HSO3-]/1.33 = 1.5*10^-2

So, 0.02*(1.33x-1.33xy)/(1.33-1.33x) = 0.02*x(1-y)/(1-x) = 0.015

Assuming y <<1 we can neglect it compared to 1

so, 0.02x/(1-x) = 0.015

0.02x = 0.015 - 0.015x

so, x = 0.015/0.0315 = 0.4286

So, [H2SO3] = 1.33-1.33x = 1.33 - 1.33*0.4286 = 0.76 M

and [HSO3-] = 1.33x = 1.33*0.4286 = 0.57 M

Also, for second dissociation we have

HSO3- -> H+ + SO32-

I 1.33x 1.33x 0

C -1.33xy +1.33xy +1.33xy

E 1.33x-1.33xy 1.33x+1.33xy 1.33xy

Ka2 = [H+][SO32-]/[HSO3-] = 6.3*10^-8

= 0.02*1.33xy/(1.33x-1.33xy) = 0.02*y/(1-y) = 6.3*10^-8

or y/(1-y) = 3.15*10^-6 or y = 3.15*10^-6 as y<<1 we can neglect it compared to 1

So, [SO3-] = 1.33*x*y = 1.33*0.4286*3.15*10^-6 = 1.795*10^-6  M or 1.8*10-6 M