2.4.1. Measurement of the Conductivity of Ionic Solutions

We know that accurate measurement of an unknown resistance can be performed on a Wheatstone bridge. However, for measuring the resistance of an ionic solution we face two problems. Firstly, passing direct current (DC) changes the composition of the solution. Secondly, a solution cannot be connected to the bridge like a metallic wire or other solid conductor.

When measuring the conductivity of ionic solutions, we encounter two main challenges. First, if we use direct current (DC) to measure resistance, it can change the concentration of ions in the solution over time, leading to inaccurate measurements. Second, ionic solutions lack the solid structure of metals, making it difficult to connect them to traditional resistance measuring devices, such as a Wheatstone bridge, in the same way we would connect a wire.

Think of it like trying to measure the flow of water through a flexible garden hose. If you suddenly change the pressure (like using DC), it can cause the water to either flow faster or create bubbles that change the amount of water, skewing any measurements. Additionally, you can’t just hook various hoses to a pressure gauge like you would with solid pipes.

The first difficulty is resolved by using an alternating current (AC) source of power. The second problem is solved by using a specially designed vessel called conductivity cell.

To address the issue of composition change in the ionic solution due to direct current, we use alternating current (AC). AC makes the direction of current flow reverse periodically, which helps to maintain a stable ion concentration in the solution. To measure the conductivity accurately, we also use a special container known as a conductivity cell that contains the ionic solution. This cell is specifically designed for measuring the conductivity of liquids.

Consider how a fluctuating breeze can keep a kite flying steadily in the air. Similarly, the alternating current helps maintain a steady environment for ions in the solution, just as the wind keeps the kite flying without it getting tangled or falling.

It consists of two platinum electrodes coated with platinum black (finely divided metallic Pt is deposited on the electrodes electrochemically). These have area of cross section equal to ‘A’ and are separated by distance ‘l’. Therefore, solution confined between these electrodes is a column of length l and area of cross section A.

A conductivity cell is constructed using two platinum electrodes, which are coated with a form of platinum known as platinum black. This coating increases the surface area of the electrodes, enhancing their ability to interact with the solution. The electrodes are a fixed distance apart (length ‘l’), and the area of the electrodes’ cross-section is denoted as ‘A’. The ionic solution fills the space between the electrodes, creating a defined column where conductivity can be effectively measured.

You can think of the conductivity cell like a pair of long straws placed into a liquid. The distance between the ends of the straws is constant, and the liquid flows through them, allowing you to measure different properties, just like how the conductivity is measured in the solution between the electrodes.

The resistance of such a column of solution is then given by the equation: R = r * (l/A). The quantity l/A is called cell constant denoted by the symbol, G*.

The resistance (R) of the column of ionic solution can be calculated using the relationship that relates resistance to resistivity (r), which depends on how well the solution conducts electricity. The formula is R = r * (l/A), where ‘l’ is the length of the solution column and ‘A’ is the area of cross-section of the electrodes. The ratio l/A is known as the cell constant (G*), which is essential in determining the conductivity of an unknown solution once the resistance is measured.

Imagine measuring how easily a liquid flows through a pipe. The longer and narrower the pipe, the more resistance you'll face. This idea helps us understand resistance in solutions; if we know how long the path is and how wide it is, we can predict how 'easy' it is for electricity to flow through it as well.

The cell constant is usually determined by measuring the resistance of the cell containing a solution whose conductivity is already known. For this purpose, we generally use KCl solutions whose conductivity is known accurately at various concentrations.

To determine the cell constant (G*), we measure the resistance of the conductivity cell filled with a known concentration of potassium chloride (KCl). KCl solutions provide reliable conductivity values at various concentrations. By knowing both the resistance measured and the known conductivity of the KCl solution, we can calculate the cell constant.

It's like having a standard measurement (like a ruler) that everyone can use. If you measure how long an object is with your ruler (the KCl solution), then measure that object with another altered ruler (the conductivity cell), you can find out how accurate your new ruler is by comparing the two lengths.

Once the cell constant is determined, we can use it for measuring the resistance or conductivity of any solution. The set up for the measurement of the resistance is shown in Fig. 2.5.

After determining the cell constant, we can apply it to any ionic solution's resistance measurement using the same apparatus. The setup includes the conductivity cell to hold the solution, along with resistors and an AC source to assess the resistance accurately. Once we have this resistance, we can easily calculate the conductivity of the solution using the previously determined cell constant.

Think of a speedometer in your car—once you have the baseline speed recorded on a straight road, you can easily measure how fast or slow you’re going on different roads using that same reading as a reference.

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