Answer:
pH = 2.96
Explanation:
∴ Ka = 6.5 E-5 = [H3O+][C6H5COO-] / [C6H5COOH]
prior to adding C6H5COONa:
⇒ C C6H5COONa = 0 M = [Na+]
∴ mass balance:
⇒ C C6H5COOH = [C6H5COOH] + [C6H5COO-] = 0.0200 M
⇒ [C6H5COOH] = 0.0200 - [C6H5COO-]
charge balance:
⇒ [H3O+] = [C6H5COO-]
⇒ [C6H5COOH] = 0.0200 - [H3O+]
⇒ Ka = [H3O+]² / (0.0200 - [H3O+]) = 6.5 E-5
⇒ [H3O+]² + 6.5 E-5[H3O+] - 1.3 E-6 = 0
⇒ [H3O+] = 1.108 E-3 M
∴ pH = - Log [H3O+]
⇒ pH = 2.9554 = 2.96
The pH of the benzoic acid solution prior to adding sodium benzoate is 2.96.
pH means potential hydrogen. The pH tells how acidic or basic a solution is.
Given,
For benzoic acid
[tex]\bold{C_6H_5COOH \rightarrow C_6H_5COO- + H_3O+}[/tex]
The ka value will be
[tex]\bold{6.5 E-5 = [H_3O+][C_6H_5COO-] / [C_6H_5COOH]}[/tex]
For sodium benzoate
[tex]\bold{C_6H_5COONa \rightarrow C_6H_5COO- + Na+}[/tex]
The Mass balance
[tex]\bold{ C_6H_5COOH [C_6H_5COOH] + [C_6H_5COO-] =0.0200\; M}\\\\\\\bold{[C_6H_5COOH] = 0.0200 - [C_6H_5COO-]}[/tex]
The charge balance
[tex][H_3O+] = [C_6H_5COO-] =[C_6H_5COOH] = 0.0200 - [H_3O+][/tex]
[tex]\bold{Ka =\dfrac{[H_3O+]²}{ (0.0200 - [H_3O+]) } = 6.5 E-5}[/tex]
[tex][H_3O+]^2+ 6.5 E-5[H_3O+] - 1.3 E-6 = 0\\[/tex]
[tex][H_3O+] = 1.108 E-3 M\\\\pH = - Log [H_3O+]\\\\pH = 2.9554 = 2.96[/tex]
Thus, the pH is 2.96.
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