According to the EK answer key, it says that the correct answer choice is C. They solved the problem using Kb
set up the solution as such
Kb = [OH-][H2CO3] / [HCO3]
0.25x10^-7 = [x][x]/ [1-x]
2.5 x10^8 = x^2
1.5 x10^-4 = x
The pOH = btw 3 & 4. Subtract from 14, the pH = btw 10 & 11.
Can you see where my confusion stems from? I don't understand why they even bothered to give us the Ka value if they were going to be using a Kb value to solve the problem. The issue is that I have no idea where they got a Kb value of 0.25x10^7 from or the motivation behind using Kb.
the Ka or Kb can be found by using the formula 1x10^-14=[Ka][Kb]...but to answer the question.
1)find the molarity which is 1mole/1liter= 1M of carbonic acid
2)set up an ice table for the reaction
H2CO3 H2O <-> H3O+ HCO3-
Initial concentration 1M n/a 0 0
Change concentration -x n/a +x +x
Equilbrium concentration 1M-x n/a x x
3)set up the equation and plug in values
Products/reactants=Ka
[H3O+]^1[HCO3-]^1/[H2CO3]^1=Ka
[x]^1[x]^1/[1-x]^1=4.3*10^-7 u can drop the -x from the denominator
which leaves u with the expression [x]^2/[1]=4.3*10^-7
solve for x...this x value equals 6.55*10^-4...looking back at your ice table u see that x is the concentration of H3O+ (H+) concentration...
plug in value into -log[H3O+]=pH and ur answer is 3.18.
BUT, the work ive shown u is for carbonic acid (H2CO3), the question is asking u about the conjugate base(HCO3-)...so the question is saying u have 1M of HCO3- not H2CO3. so u have to do the same thing ive shown above now using HCO3- but also using the Kb.
1)find the molarity which is 1mole/1liter= 1M of HCO3-
2)set up an ice table for the reaction
HCO3- H2O <-> OH- H2CO3
Initial concentration 1M n/a 0 0
Change concentration -x n/a +x +x
Equilbrium concentration 1M-x n/a x x
3)set up the equation and plug in values
Products/reactants=Kb
[OH-]^1[H2CO3]^1/[HCO3-]^1=Kb
[x]^1[x]^1/[1-x]^1=2.3*10^-8 u can drop the -x from the denominator
which leaves u with the expression [x]^2/[1]=2.3*10^-8
solve for x...this x value equals 1.52*10^-4..looking back at your ice table u see that x is the concentration of OH-concentration...
plug in value into -log[OH-]=pOH and ur answer is 3.81.
to get the pH, use pH+pOH=14 and ur
pH will be 10.19