Respuesta :
The molarity of NaOH for the addition of 10.0 mL to result in an [tex]E^o_{cell}[/tex] of 0.340 V is 8.2 × 10⁻⁴ M
What is a concentration cell?
Concentration cells are electrochemical cells made up of two half-cells with identical electrodes but different concentrations.
The more concentrated half cell is diluted and the less concentrated half cell has its concentration boosted while the cell as a whole work to achieve equilibrium through the transmission of electrons between these two half cells.
A potential difference is thus produced as the cell progresses towards chemical equilibrium.
Use the Nernst equation to determine the copper ion concentration in the half-cell containing the hydroxide ion.
[tex]E_{cell} = E^o_{cell}-\frac{0.0591}{n} log\frac{[Cu^{2+}]_{hydroxide}}{[Cu^{2+}]_{original} }[/tex]
[tex]0.340 = 0.00 -\frac{0.0591}{n} log\frac{[Cu^{2+}]_{hydroxide}}{0.0100 }\\\\\\-11.4864 = log\frac{[Cu^{2+}]_{hydroxide}}{0.0100}[/tex]
3.2622 × 10⁻¹² = [tex]\frac{[Cu^{2+}]_{hydroxide}}{0.0100}[/tex]
[tex]{[Cu^{2+}]_{hydroxide}}\\[/tex] = 3.2622 × 10⁻¹⁴
Now use the [tex]K_{sp[/tex]relationship:
[tex]K_{sp[/tex] = [Cu²⁺][OH⁻]² = 2.2 x 10⁻²⁰
[tex]K_{sp[/tex]= 2.2 x 10⁻²⁰ = [3.2622257 x 10⁻¹⁴][OH⁻]²
[OH⁻]² = 6.743862 x 10⁻⁷
[OH⁻] = 8.2121 x 10⁻⁴ = 8.2x10⁻⁴ M OH⁻
= 8.2x10⁻⁴ M NaOH
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