### Worksheet: Acid base problems - AP levelProblems 1 - 10

Problem #1: Calculate the pH of the solution that results when 40.0 mL of 0.100 M NH3 is:

a) Diluted with 20.0 mL of distilled water.
b) Mixed with 20.0 mL of 0.200 M HCl solution.
c) Mixed with 20.0 mL of 0.200 M NH4Cl

Solution to part (a):

1) Use the dilution equation:

M1V1 = M2V2

(0.100 mol/L) (0.040 L) = (x) (0.060 L)

x = 0.0667 M

2) Use the Kb for ammonia to determine pH:

Kb = ([NH4+] [OH¯]) / [NH3]

1.77 x 10¯5 = (x) (x) / (0.0667 - x)

Remember to ignore the x in 0.0667 - x.

x = 0.001086278 M (a few guard digits)

pOH = - log 0.001086278 = 2.964

pH = 11.036

Solution to part (b) and (c): Someday!

Problem #2: How many grams of ammonia are needed to make 1.25 L solution with a pH of 11.68?

Solution:

1) Use the pH to get the hydroxide ion concentration:

pH = 11.68

pOH = 14.00 - 11.68 = 2.32

[OH¯] = 10¯pOH = 10¯2.32

[OH¯] = 4.7863 x 10¯3

2) Use the Kb expression to get the [NH3]:

Kb = ([NH4+] [OH¯]) / [NH3]

1.77 x 10¯5 = (4.7863 x 10¯3) (4.7863 x 10¯3) / (x)

x = 1.294275 M (guard digits!)

3) Grams needed for 1.25 L

MV = g/molar mass

(1.294275 mol/L) (1.25 L) = x/17.031 g/mol

x = 27.6 g

Problem #3: Calculate the pH of a formic acid solution that contains 1.45% formic acid by mass. (Assume a density of 1.01 g/mL for the solution.)

Solution:

1) Calculate volume of 100.0 g of solution:

100.0 g divided by 1.01 g/mL = 99.01 mL

2) Calculate molarity of 1.45% solution of HCOOH:

1.45 g divided by 46.025 g/mol = 0.0315 mol

0.0315 mol / 0.09901 L = 0.318 M

3) Calculate [H+] in 0.318 M HCOOH solution:

1.8 x 10-4 = [(x) (x)] / 0.318

x = 7.5657 x 10-3 M (kept a couple guard digits)

4) Calculate pH:

-log 7.5657 x 10-3 = 2.12

Problem #4: A buffer solution contains 0.384 M KHCO3 and 0.239 M Na2CO3. If 0.0464 moles of potassium hydroxide are added to 225.0 mL of this buffer, what is the pH of the resulting solution ? (Assume that the volume does not change upon adding potassium hydroxide.)

Solution:

1) Calculate moles of bicarbonate and carbonate:

HCO3¯: (0.384 mol/L) (0.2250 L) = 0.0864 mol
CO32¯: (0.239 mol/L) (0.2250 L) = 0.053775 mol

2) The hydroxide reacts with the acid (the bicarbonate):

HCO3¯ decreases: 0.0864 - 0.0464 = 0.0400 mol
CO32¯ increases: 0.053775 + 0.0464 = 0.100175 mol

3) Need pKa of bicarbonate:

Ka of HCO3¯ is the same as the Ka2 of H2CO3.

Ka of HCO3¯ = 4.7 x 10¯11

pKa = 10.252

4) Use Henderson-Hasselbalch Equation:

pH = 10.328 + log (0.100 / 0.04)

pH = 10.328 + 0.398 = 10.726

Problem #5: A buffer solution contains 0.348 M ammonium chloride and 0.339 M ammonia. If 0.0248 moles of hydrochloric acid are added to 125.0 mL of this buffer, what is the pH of the resulting solution? (Assume that the volume does not change upon adding hydrochloric acid.)

Solution:

A solution on video is provided for this problem.

Problem #6: How many mL of 4.50 M sodium hydroxide must be added to 250.0 mL of a 0.200 M acetic acid solution to make a buffer with pH = 5.000?

Solution:

1) Use H-H Equation to determine required ratio of acetate to acid in solution:

5.000 = 4.752 + log [base] /[acid]

log [base] /[acid] = 0.248

[base] /[acid] = 1.77

2) Determine molar amount of base required to get pH = 5.000 (for convenience, I'm going to use 1.00 L. I'll go to 250 mL at the end of this step):

1.77x + x = 0.200

x = 0.0722 mol (this is acetic acid needed in the solution)

0.200 - 0.0722 = 0.1278 mol of base required

0.1278 /4 = 0.03195 mol of acetate required in 250 mL

3) Determine volume of NaOH solution required:

4.50 mol/L = 0.03195 mol / x

x = 0.0071 L = 7.1 mL

4) Check everything:

[acetic acid] = 0.01805 mol / 0.2571 L = 0.070206 M

[acetate] = 0.03195 mol / 0.2571 L = 0.12427 M

pH = 4.752 + log (0.12427 / 0.070206)

pH = 4.752 + log 1.77

pH = 4.752 + 0.248 = 5.000

Problem #7: If in a solution 10[H3O+] = [OH¯] then the pH of the solution is:

Solution:

1) Let:

[H3O+] = x
[OH¯] = y

2) Therefore, two equations in two unknowns:

10x = y

and

xy = 1.00 x 10¯14

3) Rearrange the second equation:

y = (1.00 x 10¯14) / x

4) Substitute into the first equation:

10x = (1.00 x 10¯14) / x

5) Rearrange and solve:

10x2 = 1.00 x 10¯14

x2 = 1.00 x 10¯15

x = 3.16 x 10¯8 M

6) Compute the pH:

pH = -log 3.16 x 10¯8 = 7.5

Problem #8: The solubility of CO2(g) in pure water is 0.0037 mol/L. Assuming that dissolved CO2 is in the form of H2CO3(aq), what is the pH of a 0.0037 M solution of dissolved CO2? Ka1 for H2CO3 = 4.3 x 10-7

Solution:

1) The relevant chemical equation is:

H2CO3 ⇌ H+ + HCO3¯

2) Substituting into the Ka expression, we find:

4.3 x 10-7 = [(x) (x)] / 0.0037

x = 3.989 x 10-5 M

3) Determine the pH:

pH = - log [H+] = -log 3.989 x 10-5

pH = 4.40 (to two sig figs)

Problem #9: A 0.484 g sample of impure NH4Br is treated with 25.00 mL of 0.2050 M NaOH and heated to drive off the NH3. The unreacted NaOH in the reaction mixture after heating required 9.95 mL of 0.0525 M H2C2O4 to neutralize. How many grams of NH4Br were in the original sample?

Solution:

1) Determine moles of NaOH added to amonium bromide solution:

(0.2050 mol/L) (0.02500 L) = 5.125 x 10¯3 mol

Keep in mind that only some of this NaOH reacted.

2) Determine moles of oxalic acid that reacted with excess NaOH:

(0.0525 mol/L) (0.00995 L) = 5.22375 x 10¯4 mol

3) Determine moles of unreacted NaOH:

This reaction:
H2C2O4(aq) + 2NaOH(aq) ---> Na2C2O4 + 2H2O(l)
demonstrates a 1:2 molar ratio between oxalic acid and NaOH.

Therefore, we multiply the oxalic acid amount by two:

5.22375 x 10¯4 mol x 2 = 1.04475 x 10¯3 mol
to determine the amount of NaOH that did not react with the ammonium bromide.

4) Determine moles of NaOH that did react with NH4Br:

5.125 x 10¯3 mol minus 1.04475 x 10¯3 mol = 4.08025 x 10¯3 mol

5) Determine grams of NH4Br:

4.08025 x 10¯3 mol times 97.943 g/mol = 0.399632 g

To three sig figs, this is 0.400 g

Example #10: If 0.50 moles Ca(OH)2 is slurried in 0.50 L deionized water and treated with 0.50 moles of CO2 gas in a closed system, the liquid phase of this system will have a pH closest to what value?

Solution:

After the Ca(OH)2 and the CO2 react, we are left with some calcium carbonate, an insoluble substance. However, from the Ksp of CaCO3, we can calculate the approximate molarity of carbonate in the aqueous phase. Please see here for a discussion:

I will use the 5.5 x 10-5 M from the above link.

Carbonate is the salt of a weak acid and so it hydrolyzes in solution:

CO32- + H2O ⇌ HCO3- + OH-

To describe that system, we require the Kb1 of carbonate, which we get from the Ka2 of carbonic acid, which is 4.7 x 10-11, from here.

So the Kb1 of carbonate is 2.13 x 10-4 (from KaKb = Kw)

We can now calculate the [OH-] in our calcium carbonate solution:

[OH-] = SQRT[(2.13 x 10-4) (5.5 x 10-5)] = 0.000108 M

The pOH is just under 4, which makes the pH be just over 10.