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Q, LON-CAPA Titration ofi × O lor capasa yo kuca/res stuehem215 problems lecture

ID: 587507 • Letter: Q

Question

Q, LON-CAPA Titration ofi × O lor capasa yo kuca/res stuehem215 problems lecture acidbase/titrwacid sba mL of 0.100-M hydrogen cyanide (Ka-6.20x10-10) is titrated with 0.100-M NaOH What is the initial pH of the hydrogen cyanide solution? Tries 0/5 What is the pH of the solution after 14.0 mL NaOH has been added? Submit Answer Tries o/5 What is the pH of the solution after a total of 17.5 ml NaOH has been added? Submit Answer Tries 0/5 What is the pH of the solution after a total of 21.0 mL NaOH has been added? Submit Answer Tries 0/5 What is the pH of the solution after a total of 35.0 mL NaOH has been added? Submit Answer Tries o/S What is the pH of the solution after a total of 42.0 mL NaOH has been added? Submit Answer Tries 0/s Post Discussion Type here to search sc

Explanation / Answer

1)when 0.0 mL of NaOH is added

Lets write the dissociation equation of HCN

HCN -----> H+ + CN-

0.1 0 0

0.1-x x x

Ka = [H+][CN-]/[HCN]

Ka = x*x/(c-x)

Assuming small x approximation, that is lets assume that x can be ignored as compared to c

So, above expression becomes

Ka = x*x/(c)

so, x = sqrt (Ka*c)

x = sqrt ((6.2*10^-10)*0.1) = 7.874*10^-6

since c is much greater than x, our assumption is correct

so, x = 7.874*10^-6 M

we have below equation to be used:

pH = -log [H+]

= -log (7.874*10^-6)

= 5.10

2)when 14.0 mL of NaOH is added

we have:

Molarity of HCN = 0.1 M

Volume of HCN = 35 mL

Molarity of NaOH = 0.1 M

Volume of NaOH = 14 mL

mol of HCN = Molarity of HCN * Volume of HCN

mol of HCN = 0.1 M * 35 mL = 3.5 mmol

mol of NaOH = Molarity of NaOH * Volume of NaOH

mol of NaOH = 0.1 M * 14 mL = 1.4 mmol

We have:

mol of HCN = 3.5 mmol

mol of NaOH = 1.4 mmol

1.4 mmol of both will react

excess HCN remaining = 2.1 mmol

Volume of Solution = 35 + 14 = 49 mL

[HCN] = 2.1 mmol/49 mL = 0.0429M

[CN-] = 1.4/49 = 0.0286M

They form acidic buffer

acid is HCN

conjugate base is CN-

Ka = 6.2*10^-10

pKa = - log (Ka)

= - log(6.2*10^-10)

= 9.208

we have below equation to be used:

This is Henderson–Hasselbalch equation

pH = pKa + log {[conjugate base]/[acid]}

= 9.208+ log {2.857*10^-2/4.286*10^-2}

= 9.03

3)when 17.5 mL of NaOH is added

we have:

Molarity of HCN = 0.1 M

Volume of HCN = 35 mL

Molarity of NaOH = 0.1 M

Volume of NaOH = 17.5 mL

mol of HCN = Molarity of HCN * Volume of HCN

mol of HCN = 0.1 M * 35 mL = 3.5 mmol

mol of NaOH = Molarity of NaOH * Volume of NaOH

mol of NaOH = 0.1 M * 17.5 mL = 1.75 mmol

We have:

mol of HCN = 3.5 mmol

mol of NaOH = 1.75 mmol

1.75 mmol of both will react

excess HCN remaining = 1.75 mmol

Volume of Solution = 35 + 17.5 = 52.5 mL

[HCN] = 1.75 mmol/52.5 mL = 0.0333M

[CN-] = 1.75/52.5 = 0.0333M

They form acidic buffer

acid is HCN

conjugate base is CN-

Ka = 6.2*10^-10

pKa = - log (Ka)

= - log(6.2*10^-10)

= 9.208

we have below equation to be used:

This is Henderson–Hasselbalch equation

pH = pKa + log {[conjugate base]/[acid]}

= 9.208+ log {3.333*10^-2/3.333*10^-2}

= 9.21

4)when 21.0 mL of NaOH is added

we have:

Molarity of HCN = 0.1 M

Volume of HCN = 35 mL

Molarity of NaOH = 0.1 M

Volume of NaOH = 21 mL

mol of HCN = Molarity of HCN * Volume of HCN

mol of HCN = 0.1 M * 35 mL = 3.5 mmol

mol of NaOH = Molarity of NaOH * Volume of NaOH

mol of NaOH = 0.1 M * 21 mL = 2.1 mmol

We have:

mol of HCN = 3.5 mmol

mol of NaOH = 2.1 mmol

2.1 mmol of both will react

excess HCN remaining = 1.4 mmol

Volume of Solution = 35 + 21 = 56 mL

[HCN] = 1.4 mmol/56 mL = 0.025M

[CN-] = 2.1/56 = 0.0375M

They form acidic buffer

acid is HCN

conjugate base is CN-

Ka = 6.2*10^-10

pKa = - log (Ka)

= - log(6.2*10^-10)

= 9.208

we have below equation to be used:

This is Henderson–Hasselbalch equation

pH = pKa + log {[conjugate base]/[acid]}

= 9.208+ log {3.75*10^-2/2.5*10^-2}

= 9.38

5)when 35.0 mL of NaOH is added

we have:

Molarity of HCN = 0.1 M

Volume of HCN = 35 mL

Molarity of NaOH = 0.1 M

Volume of NaOH = 35 mL

mol of HCN = Molarity of HCN * Volume of HCN

mol of HCN = 0.1 M * 35 mL = 3.5 mmol

mol of NaOH = Molarity of NaOH * Volume of NaOH

mol of NaOH = 0.1 M * 35 mL = 3.5 mmol

We have:

mol of HCN = 3.5 mmol

mol of NaOH = 3.5 mmol

3.5 mmol of both will react to form CN- and H2O

CN- here is strong base

CN- formed = 3.5 mmol

Volume of Solution = 35 + 35 = 70 mL

Kb of CN- = Kw/Ka = 1*10^-14/6.2*10^-10 = 1.613*10^-5

concentration ofCN-,c = 3.5 mmol/70 mL = 0.05M

CN- dissociates as

CN- + H2O -----> HCN + OH-

0.05 0 0

0.05-x x x

Kb = [HCN][OH-]/[CN-]

Kb = x*x/(c-x)

Assuming small x approximation, that is lets assume that x can be ignored as compared to c

So, above expression becomes

Kb = x*x/(c)

so, x = sqrt (Kb*c)

x = sqrt ((1.613*10^-5)*5*10^-2) = 8.98*10^-4

since x is comparable c, our assumption is not correct

we need to solve this using Quadratic equation

Kb = x*x/(c-x)

1.613*10^-5 = x^2/(5*10^-2-x)

8.065*10^-7 - 1.613*10^-5 *x = x^2

x^2 + 1.613*10^-5 *x-8.065*10^-7 = 0

Let's solve this quadratic equation

Comparing it with general form: (ax^2+bx+c=0)

a = 1

b = 1.613*10^-5

c = -8.065*10^-7

solution of quadratic equation is found by below formula

x = {-b + (b^2-4*a*c)}/2a

x = {-b - (b^2-4*a*c)}/2a

b^2-4*a*c = 3.226*10^-6

putting value of d, solution can be written as:

x = {-1.613*10^-5 + (3.226*10^-6)}/2

x = {-1.613*10^-5 - (3.226*10^-6)}/2

solutions are :

x = 8.9*10^-4 and x = -9.061*10^-4

since x can't be negative, the possible value of x is

x = 8.9*10^-4

[OH-] = x = 8.9*10^-4 M

we have below equation to be used:

pOH = -log [OH-]

= -log (8.9*10^-4)

= 3.0506

we have below equation to be used:

PH = 14 - pOH

= 14 - 3.0506

= 10.95

6)when 42.0 mL of NaOH is added

we have:

Molarity of HCN = 0.1 M

Volume of HCN = 35 mL

Molarity of NaOH = 0.1 M

Volume of NaOH = 42 mL

mol of HCN = Molarity of HCN * Volume of HCN

mol of HCN = 0.1 M * 35 mL = 3.5 mmol

mol of NaOH = Molarity of NaOH * Volume of NaOH

mol of NaOH = 0.1 M * 42 mL = 4.2 mmol

We have:

mol of HCN = 3.5 mmol

mol of NaOH = 4.2 mmol

3.5 mmol of both will react

excess NaOH remaining = 0.7 mmol

Volume of Solution = 35 + 42 = 77 mL

[OH-] = 0.7 mmol/77 mL = 0.0091 M

we have below equation to be used:

pOH = -log [OH-]

= -log (9.091*10^-3)

= 2.0414

we have below equation to be used:

PH = 14 - pOH

= 14 - 2.0414

= 11.96

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