7.70. The ionization constant of benzoic acid is 6.46×10⁻⁵ and Ksp for silver benzoate is 2.5×10⁻¹³. How many times is silver benzoate more soluble in a buffer of pH= 3.19 compared to its solubility in pure water?

<p>Since pH=3.19, &nbsp;</p><p> [H3O⁺]=6.46×10⁻⁴M</p><p>C₆H₅COOH+H₂O↔C₆H₅COO⁻+H₃O&nbsp;</p><p>K_a= [C₆H₅COO⁻] [H₃O⁺] / [C₆H₅COOH]&nbsp;</p><p> [C₆H₅COOH] / [C₆H₅COO⁻]= [H₃O⁺] / Ka=6.46×10⁻⁴ / 6.46×10⁻⁵=10</p><p>Let the solubility of C₆H₅COOAg be xmol/L.</p><p>Then, </p><p> [Ag⁺]=x</p><p> [C₆H₅COOH]+ [C₆H₅COO⁻]=x&nbsp;</p><p>10 [C₆H₅COO⁻]+ [C₆H₅COO⁻]=x&nbsp;</p><p> [C₆H₅COO⁻]=x / 11&nbsp;</p><p>K_sp = [Ag⁺] [C₆H₅COO⁻]&nbsp;</p><p>= &gt;2.5×10⁻¹3=x (x / 11)</p><p>= &gt;x=1.66×10⁻⁶mol/L</p><p>Thus, the solubility of silver benzoate in a pH3.19 solution is 1.66×10⁻⁶mol/L.</p><p>Now, let the solubility of C₆H₅COOAg be x′mol/L.</p><p>Then, [Ag⁺]=x′Mand [C6H5COO⁻]=x′M</p><p>K_sp= [Ag⁺] [C6H5COO⁻]&nbsp;</p><p>Ksp= (x′)²</p><p>x′= (Ksp)^1/2= (2.5×10⁻¹³)^1/2= 5×10⁻⁷mol/L</p><p>∴x / x′= (1.66×10⁻⁶) / (5×10⁻⁷) =3.32</p><p>Hence, C₆H₅COOAg is approximately 3.317 times more soluble in a low pH solution.</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment