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You determine that it takes 26.0 mL of base to neutralize a sample of your unknown acid solution. The pH of the solution was 7.82 when exactly 13 mL of base had been added. What is the pKa of your unknown acid?

User Yoavf
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1 Answer

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Complete Question

You determine that it takes 26.0 mL of base to neutralize a sample of your unknown acid solution. The pH of the solution was 7.82 when exactly 13 mL of base had been added, you notice that the concentration of the unknown acid was 0.1 M. What is the pKa of your unknown acid?

Answer:

The pK_a value is
pK_a =7.82

Step-by-step explanation:

From the question we are told

The volume of base is
V_B = 26.mL = 0.0260L

The pH of solution is
pH = 7.82

The concentration of the acid is
C_A = 0.1M

From the pH we can see that the titration is between a strong base and a weak acid

Let assume that the the volume of acid is
V_A = 18mL= 0.018L

Generally the concentration of base


C_B = (C_AV_A)/(C_B)

Substituting value


C_B = (0.1 * 0.01800)/(0.0260)


C_B= 0.0692M

When 13mL of the base is added a buffer is formed

The chemical equation of the reaction is


HA_((aq)) + OH^-_((aq)) --------> A^(+)_((aq)) + H_2 O_((l))

Now before the reaction the number of mole of base is


No \ of \ moles[N_B] = C_B * V_B

Substituting value


N_B = 0.01300 * 0.0692


= 0.0009 \ moles

Now before the reaction the number of mole of acid is


No \ of \ moles = C_B * V_B

Substituting value


N_A = 0.01800 *0.1


= 0.001800 \ moles

Now after the reaction the number of moles of base is zero i.e has been used up

this mathematically represented as


N_B ' = N_B - N_B = 0

The number of moles of acid is


N_A ' = N_A - N_B


= 0.0009\ moles

The pH of this reaction can be mathematically represented as


pH = pK_a + log ([base])/([acid])

Substituting values


7.82 = pK_a +log (0.0009)/(0.0009)


pK_a =7.82

User Bere
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