Question

The resistance of \(0.1 \mathrm{~N}\) solution of formic acid is \(200 \mathrm{ohm}\) and cell constant is \(2.0 \mathrm{~cm}^{-1}\). The equivalent conductivity (in \(\mathrm{Scm}^{2} \mathrm{eq}^{-1}\) ) of \(0.1 \mathrm{~N}\) formic acid is : (a) 100 (b) 10 (c) 1 (d) none of these

Short answer

100 \( \mathrm{Scm}^{2} \mathrm{eq}^{-1} \)

Step-by-step solution

Understand The Concepts Involved

Equivalent conductivity \( \Lambda_m \) is a measure of the conductivity of an electrolyte solution divided by the molar concentration of the electrolyte. It is given by the formula \( \Lambda_m = \frac{k}{C} \) where \( k \) is the specific conductivity of the solution and \( C \) is the molar concentration. To find \( k \) we use the cell constant \( G^* \) and resistance \( R \) by the relation \( k = \frac{G^*}{R} \) since \( G^* \) is given in \( \mathrm{cm}^{-1} \) and \( R \) in ohms.

Calculate Specific Conductivity \( k \) of the Solution

Using the formula \( k = \frac{G^*}{R} \) given the cell constant \( G^* = 2.0 \mathrm{~cm}^{-1} \) and resistance \( R = 200 \mathrm{ohm} \) we calculate \( k = \frac{2.0}{200} \) which equals \( 0.01 \mathrm{S/cm} \) (since \( 1/S = 1/ohm \) by definition of siemens).

Convert the Concentration from Normality to Molarity

Since normality (N) of a solution is equal to its molarity (M) multiplied by the number of equivalents per mole, and formic acid is a monoprotic acid (only donates one proton per molecule), the molarity and normality are equal. Therefore, the molarity \( C = 0.1 \mathrm{N} = 0.1 \mathrm{M} \) (where M stands for molar, i.e., moles per liter).

Calculate Equivalent Conductivity \( \Lambda_m \) of the Solution

With \( k = 0.01 \mathrm{S/cm} \) and \( C = 0.1 \mathrm{M} \) use the formula for equivalent conductivity \( \Lambda_m = \frac{k}{C} \) to find \( \Lambda_m = \frac{0.01}{0.1} = 0.1 \mathrm{Scm^2/mol} \) which is equivalent to \( 0.1 \times 1000 = 100 \mathrm{Scm^2/eq} \) since there are 1000 milliequivalents in 1 equivalent.

Key concepts

Electrolyte Solution Conductivity

Conductivity of an electrolyte solution refers to its ability to conduct electricity. It is largely dictated by the presence of ions in the solution, which move to transport electrical charge. When an electrical field is applied to the solution, these ions respond by moving towards the opposite-charged electrode, thus creating an electric current. The more ions present, the higher the conductivity.

Conductivity can be affected by several factors, including the type of electrolyte, the concentration of ions, and the temperature of the solution. For an educator providing content that is easy to grasp for students, it's important to highlight that conductivity is not a constant value for a given substance; it changes with concentration and temperature.

Tips to Remember:

• Higher ionic concentration usually means higher conductivity.
• Dissociation of electrolytes into ions is what allows an electrolytic solution to conduct electricity.
• Pure water has very low conductivity—what makes water a conductor is the dissolved ions it contains.

Cell Constant

The cell constant, denoted often as \( G^* \), is a unique characteristic of an electrochemical cell, which includes the electrodes and the container in which the electrolyte solution is held. It's determined by the geometry of the cell, specifically the distance between the electrodes relative to the area of the electrodes immersed in the solution.

Mathematically, the cell constant is defined as the ratio of the distance between the electrodes (d) to the cross-sectional area of the electrodes (A): \( G^* = d/A \). Its unit is usually given in centimeters inverse (cm^-1). The cell constant is crucial when converting measured resistance into specific conductivity, as seen in the example problem.

Important Notes:

• The cell constant must be known or measured to accurately determine the conductivity of a solution.
• If the cell geometry changes, the cell constant also changes.
• Cells with a higher constant are better suited for measuring low conductivities, and vice versa.

Molar Concentration

Molar concentration, or molarity, is a measure of the concentration of a solute in a solution. It's expressed in moles per liter (mol/L or M), representing the number of moles of solute dissolved in one liter of solution. Molarity is one of several ways to express concentration; others include normality, molality, and mass percent.

For simplicity and to avoid confusion, when teaching this concept, it's good to emphasize the direct relationship of molarity with the number of moles: More moles of a substance in a given volume means a higher molar concentration. A solution with a higher molar concentration will have more solute particles and may exhibit a higher conductivity if the solute is an electrolyte.

Highlighted Points:

• Increasing the molarity of an electrolyte typically increases the solution's conductivity.
• Molar concentration is crucial when calculating equivalent conductivity.
• Accurate measurement of the volume of the solution is key when determining molarity.

Specific Conductivity

Specific conductivity, denoted by \( k \), represents the ability of a specific solution to conduct electrical current. It is dependent on the ions present in that solution and their concentration, size, and charge. Specific conductivity is also affected by the temperature of the solution.

It's calculated by dividing the measured conductivity by the cell constant, \( k = \frac{measured conductivity}{G^*} \). The unit for specific conductivity is siemens per meter (S/m) or siemens per centimeter (S/cm), and it describes the conductivity of the solution itself, without taking the cell's dimensions into account.

Quick Tips:

• Specific conductivity is an intrinsic property of the solution.
• When comparing solutions, specific conductivity allows for an unbiased comparison, independent of the cells used.
• It's a key value used to calculate equivalent conductivity as seen in the provided exercise.