Suppose you wanted to produce an aqueous solution of pH = 8.80 by dissolving KNO2 in water, at what molarity?
Here is my work:
KNO2 ----> K^+ NO2-
NO2^- + H2O ---> HNO2 + OH^-
Ka= 4.5 x 10^-4
Ka*Kb=Kw
Kb=Kw/Ka
kb=10^-14/4.5 x 10^-4=2.222 x 10^-11
pH+pOH=14.00
pOH=14.00-8.80=5.20
[OH^-]=10^-(5.20)= 6.310 x 10^-6 M
OH=HNO2
Kb=[6.310 x 10^-6 M][6.310 x 10^-6 M]/[x-6.31 x 10^-6 M]
Kb*[x-6.31 x 10^-6 M]=3.981 x 10^-11 M
(3.981 x 10^-11)/(2.222 x 10^-11)=x-6.31 x 10^-6 M
1.8 M=x
x=KNO2
I obtained 1.79 M which I would round to 1.8M; however, you made a typo on line 11 counting down from the KNO2 equation line. You didn't square the 6.31E-6 in the numerator but you corrected that in the next line and you have the right number there of 3.98E-11.
Thought is correct, but just wanted to make sure. Thanks for catching the typo.
Bests
To produce an aqueous solution of pH = 8.80 by dissolving KNO2 in water, the molarity of KNO2 needed is 1.8 M.
To determine the molarity of the KNO2 solution needed to achieve a pH of 8.80, you used the following steps:
1. Recognize that KNO2 dissociates into K+ and NO2- ions in water.
2. Write the dissociation reaction of NO2- with water to form HNO2 and OH- ions.
3. Use the given ka value (4.5 x 10^-4) to find the value of the basicity constant, Kb.
4. Apply the relationship between Ka, Kb, and Kw (the self-ionization constant of water) to calculate Kb.
5. Use the relationship pH + pOH = 14.00 to determine the pOH value for the solution (14.00 - 8.80 = 5.20).
6. Convert the pOH value to the hydroxide ion concentration ([OH-]) using the formula [OH-] = 10^(-pOH).
7. Recognize that [OH-] is equivalent to [HNO2] (since every HNO2 molecule dissociates into one H+ ion and one NO2- ion).
8. Write the expression for the Kb of HNO2 using the concentration of [HNO2], [OH-], and unknown concentration [x] as a variable.
9. Plug in the calculated values and solve for [x - 6.31 x 10^-6 M].
10. Use the solved value to find the final concentration of [x], which is the molarity of KNO2.
Based on your calculations, you determined that the molarity of KNO2 needed to achieve a pH of 8.80 is 1.8 M.