Consider the titration of 42.5 ml of 0.193 m hcl with 0.125 m koh. calculate the ph of the resulting solution after the following volumes of koh have been added. (assume that all solutions are at 25°c.)

When there is 0 mL of KOH added, the pH of the solution is 0.714

When there is added 3 mL of KOH, the pH of the solution is 0.764

When there is added 5 mL of KOH, the pH of the solution is 0.799

Explanation:

Step 1: Data given

Volume of 0.193 M HCl = 42.5 mL = 0.0425 L

Molarity of KOH = 0.125 M

Step 2: The balanced equation:

HCl + KOH > KCl + H2O

Step 3: pH of the solution when adding 0 mL of KOH

pH = -log[H+]

pH = -log (0.193)

pH = 0.714

Step 4: Calculate moles of HCl

Moles HCl = molarity * volume

Moles HCl = 0.193 M * 0.0425

Moles HCl = 0.0082 moles

Step 5: Adding 3 mL of KOH

When adding 3mL of KOH, the number of moles of KOH are:

Moles KOH = 0.125 M * 0.003 L

Moles KOH = 0.000375 moles

The mole ratio of the reacton is 1:1 so 0.000375 moles of KOH will react with 0.000375 moles of HCl

There will remain 0 moles of KOH

There will remain 0.0082 - 0.000375 = 0.007825 moles of HCl

The KCl formed, will not have an effect on the pH because it's a salt of a strong acid and strong base.

The final volume = 42.5 + 3 = 45.5 ml = 0.0455 L  

The new molarity of HCl = 0.007825/0.0455 = 0.172

HCl is a strong acid, this means it dissociates completely

HCl → H+ + Cl-

so [H+] = [HCl] = 0.172 M

pH = -log [H+] = -log(0.172) = 0.764

Step 6: pH when adding 5 mL of KOH

When adding 5 mL of KOH, the number of moles of KOH are:

Moles KOH = 0.125 M * 0.005 L

Moles KOH = 0.000625 moles

The mole ratio of the reacton is 1:1 so 0.000625 moles of KOH will react with 0.000625 moles of HCl

There will remain 0 moles of KOH

There will remain 0.0082 - 0.000625 = 0.007575 moles of HCl

The KCl formed, will not have an effect on the pH because it's a salt of a strong acid and strong base.

The final volume = 42.5 + 5 = 47.5 ml = 0.0475 L  

The new molarity of HCl = 0.007575/0.0475 = 0.159

HCl is a strong acid, this means it dissociates completely

HCl → H+ + Cl-

so [H+] = [HCl] = 0.159 M

pH = -log [H+] = -log(0.156) = 0.799

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