Problem 81 - Analytical Chemistry

Question

Alkali metal ions can be determined volumetrically by passing a solution of them through a cation exchange column in the hydrogen form. They displace an equivalent amount of hydrogen ions that appear in the effluent and can be titrated. How many millimoles of potassium ion are contained in a liter of solution if the effluent obtained from a \(5.00-\mathrm{mL}\) aliquot run through a cation exchange column requires \(26.7 \mathrm{~mL}\) of \(0.0506 \mathrm{M} \mathrm{NaOH}\) for titration?

Step-by-Step Solution

Answer

The solution contains 270 millimoles of potassium ions per liter.

Step 1: Determine the amount of NaOH used in titration

First, we need to calculate the number of millimoles of NaOH used in the titration. This is done by multiplying the volume of NaOH used (in liters) by its concentration:\[ ext{mmol of NaOH} = 26.7 ext{ mL} \times 0.0506 \frac{ ext{mmol}}{ ext{mL}} = (26.7 \times 0.0506) ext{ mmol} = 1.35 ext{ mmol} \]

Step 2: Relate NaOH to hydrogen ions

The millimoles of NaOH used to titrate the effluent represent an equivalent amount of hydrogen ions displaced by potassium ions in the exchange process. Hence, the millimoles of hydrogen ions is equal to the millimoles of NaOH, which is 1.35 millimoles.

Step 3: Calculate potassium ions in the aliquot

The amount of hydrogen ions displaced is equal to the amount of potassium ions present in the aliquot. Therefore, the 5.00 mL aliquot contains 1.35 millimoles of potassium ions.

Step 4: Scale up to calculate potassium ions in 1 liter of solution

Since the 1.35 millimoles of potassium ions were determined from a 5.00 mL aliquot, we need to scale it up proportionally to 1000 mL to find the concentration in one liter:\[ ext{mmol of K}^+ = rac{1000 ext{ mL}}{5 ext{ mL}} \times 1.35 ext{ mmol} = 270 ext{ mmol} \]

Key Concepts

Cation Exchange

Cation exchange is a vital process in analytical chemistry used to separate and quantify specific ions in a solution. In simple terms, this process involves the replacement or exchange of one type of cation present in the solution with another cation on an exchange material, typically a resin. The resin is usually in its hydrogen form for our exercise.

Here's how it works:

• A solution with cations passes through a column packed with the resin.
• As the solution moves through, the alkali metal ions (like potassium) replace hydrogen ions on the resin.
• The displaced hydrogen ions emerge in the effluent solution, which can be collected and measured.

The efficiency of a cation exchange depends on the selectivity of the resin and the conditions of the exchange, such as pH and flow rate. This makes cation exchange a precise method for separating specific ions from a mixture.

Volumetric Analysis

Volumetric analysis is a quantitative analytical method widely used in chemistry. It involves measuring the volume of a solution of known concentration, the titrant, required to react completely with a given sample. This method is crucial for determining the concentration of an unknown solution.

One common volumetric technique is titration, where a solution (titrant) is added to another solution containing the analyte until the reaction is complete. The point of completion is signaled by an indicator or a measurable change in the solution. This helps calculate the concentration of ions or molecules in the original sample.

In our context, volumetric analysis is used to assess the effluent from the cation exchange process. We titrate the solution with a known amount of sodium hydroxide (NaOH), determining the concentration of displaced hydrogen ions, and indirectly, the concentration of potassium ions.

Alkali Metal Ions Titration

Titrating alkali metal ions involves indirect determination due to their displacement of hydrogen ions in the solution. In our problem, the goal is to find out how much potassium ion is in a given volume of solution through titration.

Here's the step-by-step:

• Firstly, the displaced hydrogen ions in the effluent are titrated with NaOH, a strong base.
• The volume and concentration of NaOH used gives the moles of hydrogen ions titrated, previously displaced by the alkali metal ions.
• Since the number of moles of hydrogen ions equals the number of moles of alkali metal ions displaced, we can deduce the potassium ion concentration from it.

This titration method provides a reliable and efficient way to measure the concentration of alkali metals, like potassium, in complex solutions where direct analysis might be challenging.