Question

Design an Experiment Describe how you would design and perform a titration in which you use 0.250 \(\mathrm{M} \mathrm{HNO}_{3}\) to determine the molarity of a cesium hydroxide solution. Include the formula and net ionic equations.

Short answer

To determine the molarity of a cesium hydroxide (CsOH) solution using 0.250 M HNO₃, set up a titration experiment with a burette, conical flask, magnetic stirrer or glass rod, and phenolphthalein indicator. Fill the burette with HNO₃ and add a known volume of CsOH solution to the flask. Titrate the CsOH solution with the HNO₃ until the phenolphthalein indicator persists in a pink color, indicating the endpoint. Write the balanced equation and net ionic equation for the reaction: \(HNO3 + CsOH \rightarrow CsNO3 + H2O\) \(H^+ + OH^- \rightarrow H2O\) Use the formula \(M_1V_1 = M_2V_2\) with the stoichiometry of the reaction (1:1) to calculate the molarity of the CsOH solution: \(M_2 = \frac{(0.250\ M)(V_HNO3)}{25.0\ mL}\) The calculated molarity will provide the concentration of the cesium hydroxide solution.

Step-by-step solution

Understanding the Titration Reaction

A titration is a procedure used in analytical chemistry to determine the concentration of an unknown solution by reacting it with a standard solution of known concentration. In this exercise, we wish to perform a titration using 0.250 M HNO₃ as the titrant to determine the molarity of a cesium hydroxide solution that we can denote as \(x\) M CsOH. The balanced chemical equation for the reaction between HNO₃ and CsOH is: \(HNO3 + CsOH \rightarrow CsNO3 + H2O\) The net ionic equation is: \(H^+ + OH^- \rightarrow H2O\) Now that we know the reaction, we can proceed to design the experiment.

Preparing the Experimental Setup

To perform the titration, you will need the following equipment: 1. A burette: To dispense the known HNO₃ solution. 2. A conical flask or Erlenmeyer flask: To hold the unknown CsOH solution. 3. A magnetic stirrer or glass rod: To mix the reactants during the titration process. 4. Phenolphthalein indicator: To signal the endpoint of the titration. Firstly, rinse the burette with a small portion of the 0.250 M HNO₃ solution and then fill it with the same solution. Make sure to remove any air bubbles from the burette tip. Record the initial volume on the burette.

Preparing the Unknown CsOH Solution

Measure a precise volume (let's say 25.0 mL) of the unknown CsOH solution using a pipette and transfer it to the conical flask or Erlenmeyer flask. Add a few drops of phenolphthalein indicator to the flask.

Performing the Titration

Slowly dispense the HNO₃ solution from the burette into the flask containing the CsOH solution while stirring the mixture with a magnetic stirrer or glass rod. The phenolphthalein indicator will temporarily turn pink when adding the acid but will become colorless again as the mixture is stirred. This is due to the acid neutralizing the hydroxide ions. Continue adding HNO₃ until the pink color of the phenolphthalein persists even with thorough stirring. The titration has now reached its endpoint, and the titrant (HNO₃) and sample (CsOH) solutions have reacted in a stoichiometric ratio. Record the final volume of the HNO₃ solution in the burette.

Calculating the Molarity of the CsOH Solution

Using the initial and final volume readings on the burette, determine the volume of the HNO₃ solution consumed during the titration. Let's denote this volume as \(V_HNO3\). From the balanced net ionic equation, we know that the stoichiometry of the reaction is 1:1, meaning that the moles of H⁺ from HNO₃ equal the moles of OH⁻ from CsOH at the endpoint. Thus, we can use the formula: \(M_1V_1 = M_2V_2\) Where: \(M_1\) - molarity of HNO₃ (0.250 M) \(V_1\) - volume of HNO₃ used in the titration \(M_2\) - molarity of CsOH (we want to determine this) \(V_2\) - volume of CsOH solution (25.0 mL) Rearrange the formula to solve for \(M_2\): \(M_2 = \frac{M_1V_1}{V_2}\) Now, plug in the values and calculate the molarity of the CsOH solution: \(M_2 = \frac{(0.250\ M)(V_HNO3)}{25.0\ mL}\) With the calculated molarity, the concentration of the cesium hydroxide solution is determined.

Key concepts

Chemical Equation

In the realm of titration, a chemical equation is essentially a recipe that tells us what happens during the reaction between two substances. Understanding the chemical equation allows us to predict the reaction products and their quantities, which is crucial for designing experiments.

For example, in the titration scenario described, the chemical equation is: \[ \text{HNO}_3 + \text{CsOH} \rightarrow \text{CsNO}_3 + \text{H}_2\text{O} \] This equation tells us that nitric acid (HNO₃) reacts with cesium hydroxide (CsOH) to produce cesium nitrate (CsNO₃) and water (H₂O).

Understanding this equation is important as it provides a theoretical framework for the practical steps involved in the titration experiment.

Net Ionic Equation

A net ionic equation is a simplified version of the chemical equation which focuses solely on the ions that participate in forming the precipitate or product. This is particularly useful in titration as it highlights the key participants in the solution transformation.

For the reaction between HNO₃ and CsOH, the net ionic equation is: \[ \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \]This equation shows the combination of hydrogen ions (H⁺) from the acid with hydroxide ions (OH⁻) from the base to form water, which is the driving force of the reaction.

By focusing on these ions, the net ionic equation provides clarity on how titration neutralizes the base with the acid, helping to determine the endpoint of the titration.

Molarity Calculation

Calculating molarity is a crucial part of titration as it allows us to find the concentration of an unknown solution. Molarity (M) is defined as the number of moles of solute per liter of solution.

For titration calculations, the concept of molarity appears in formulas such as \[ M_1V_1 = M_2V_2 \] Where:

• \( M_1 \) is the molarity of the titrant (HNO₃ here),
• \( V_1 \) is the volume of the titrant used,
• \( M_2 \) is the molarity of the unknown solution (CsOH),
• \( V_2 \) is the volume of the unknown solution.

Through this equation, we can solve for \( M_2 \), thereby finding the molarity of the cesium hydroxide solution. This calculation is vital for achieving precise results in analytical chemistry.

Analytical Chemistry

Analytical chemistry involves the study of the composition of substances. Titration is a common analytical procedure that falls under this field, primarily used to determine the concentration of a solution.

In an analytical chemistry lab, titration is performed using precise instruments such as burettes and pipettes. These tools help ensure accuracy when measuring liquids, which is essential for valid results.

Analytical chemists use titration to evaluate substances' purity and concentration, making it a vital technique in various industries, including pharmaceuticals and environmental science. Through titration, analytical chemistry allows us to make informed decisions based on reliable quantitative data.