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The electrical resistance of a column of 0.05mol/L NaOH solution of diameter 1cm and length 50cm is 5.55×10^3Ω. Calculate its resistivity, conductivity, and molar conductivity.

User LaaasBIGL
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Final answer:

To calculate the resistivity of the NaOH solution, we can use the equation R = \(\rho\frac{L}{A}\), where R is the resistance, L is the length, and A is the cross-sectional area. The resistivity can be found by solving for \(\rho\) in the equation. The conductivity can be calculated from \(\sigma = \frac{1}{\rho}\), and the molar conductivity can be calculated using \(\Lambda_m = \frac{K_m}{C}\).

Step-by-step explanation:

We can use the formula R = \(\rho\frac{L}{A}\) to calculate the resistivity \(\rho\) of the NaOH solution. Given that the resistance R is 5.55x10^3 Ω, the length L is 50 cm, and the diameter (which is equal to the width) of the column is 1 cm, we can calculate the cross-sectional area A as follows:

\[A = \frac{\pi(d/2)^2}{4} = \frac{\pi(1/2)^2}{4} = \frac{\pi}{16} cm^2\] \[= \frac{3.14}{16} cm^2\] \[= 0.19625 cm^2\]

Now we can substitute the values into the resistivity formula and solve for \(\rho\):

\[5.55x10^3 = \rho\frac{50}{0.19625}\]

From this equation, we can solve for \(\rho\) to get the resistivity of the NaOH solution. To calculate the conductivity, we can use the equation \(\sigma = \frac{1}{\rho}\). Finally, to calculate the molar conductivity, we can use the equation \(\Lambda_m = \frac{K_m}{C}\), where \(K_m\) is the conductivity and \(C\) is the concentration of the solution.

User IndigoDelta
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