Following are data on the molar conductivity of NaOH as a function of concentration at 25°C: Find the value of Λ0 for NaOH. Compare the value obtained with the value from Table A.20.

Question

Following are data on the molar conductivity of NaOH as a function of concentration at 25°C:

[latex]concentration/mol L^{−1}[/latex]	[latex]Λ/ohm^{−1} cm^{2} mol^{−1}[/latex]
0.0010	244.5
0.0100	238.0
0.0500	227.6
0.1000	221.2
0.2000	213.0
0.5000	197.6
1.0000	178.8

Find the value of [latex]Λ_{0}[/latex] for NaOH. Compare the value obtained with the value from Table A.20.

Table A.20 Molar Conductivities and Ion Mobilities at Infinite Dilution in Water at 298.15 K
Ion	[latex]λ_{0}×10^{3}/m^{2} ohm^{-1} mol^{-1} [/latex]	[latex]u×10^{8}/m^{2} s^{-1} V^{-1}[/latex]
[latex]H^{+}[/latex]	34.982	36.25
[latex]K^{+}[/latex]	7.352	7.619
[latex]Na^{+}[/latex]	5.011	5.193
[latex]Li^{+}[/latex]	3.869	4.010
[latex]NH_{4} ^{+}[/latex]	7.34	7.61
[latex]Ca^{2+}[/latex]	11.90	6.166
[latex]OH^{-}[/latex]	19.8	20.5
[latex]Cl^{-}[/latex]	7.634	7.912
[latex]Br^{-}[/latex]	7.84	8.13
[latex]I^{-}[/latex]	7.685	7.96
[latex]NO_{3}^{+}[/latex]	7.144	7.404
Acetate,[latex]C_{2}H_{3}O^{−}_{2}[/latex]	4.09	4.24
[latex]ClO_{4}^{-}[/latex]	6.80	7.05
[latex]SO_{4^{2-}}[/latex]	15.94	8.27
From A. J. Bard and L. R. Faulkner, Electrochemical Methods,Wiley, New York, 1980, p. 67.

Accepted Answer

As indicated in Eq. (10.6.19), a plot of Λ versus [latex]c^{1/2}[/latex] for a strong electrolyte should be nearly linear at small concentrations. Such a plot is shown in Figure 10.10.

The extrapolation to zero concentration was accomplished by fitting the data to a polynomial of degree 5, since the plot is not linear over the range of concentrations given. The formula for the polynomial is shown in the figure, and the intercept was found to be

[latex]Λ_{0}=247.7 ohm^{−1} cm^{2} mol^{−1}[/latex]

From Table A.20,

[latex]Λ_{0}=λ(Na^{+})+λ(OH^{−})[/latex]

[latex]=19.8×10^{−3} ohm^{−1} m^{2} mol^{−1}+5.011×10^{−3} ohm^{−1} m^{2} mol^{−1}[/latex]

[latex]=24.8×10^{−3} ohm^{−1} m^{2} mol^{−1}=248 ohm^{−1} cm^{2} mol^{−1}[/latex]

in good agreement with the value from the extrapolation.

Table A.20 Molar Conductivities and Ion Mobilities at Infinite Dilution in Water at 298.15 K
Ion	[latex]λ_{0}×10^{3}/m^{2} ohm^{-1} mol^{-1} [/latex]	[latex]u×10^{8}/m^{2} s^{-1} V^{-1}[/latex]
[latex]H^{+}[/latex]	34.982	36.25
[latex]K^{+}[/latex]	7.352	7.619
[latex]Na^{+}[/latex]	5.011	5.193
[latex]Li^{+}[/latex]	3.869	4.010
[latex]NH_{4} ^{+}[/latex]	7.34	7.61
[latex]Ca^{2+}[/latex]	11.90	6.166
[latex]OH^{-}[/latex]	19.8	20.5
[latex]Cl^{-}[/latex]	7.634	7.912
[latex]Br^{-}[/latex]	7.84	8.13
[latex]I^{-}[/latex]	7.685	7.96
[latex]NO_{3}^{+}[/latex]	7.144	7.404
Acetate,[latex]C_{2}H_{3}O^{−}_{2}[/latex]	4.09	4.24
[latex]ClO_{4}^{-}[/latex]	6.80	7.05
[latex]SO_{4^{2-}}[/latex]	15.94	8.27
From A. J. Bard and L. R. Faulkner, Electrochemical Methods, Wiley, New York, 1980, p. 67.

Question 10.21: Following are data on the molar conductivity of NaOH as a fu...

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