Problem 108 - Chemistry Matter and Change

Question

Apply Students conducted a lab to investigate limiting and excess reactants. The students added different volumes of sodium phosphate solution \(\left(\mathrm{Na}_{3} \mathrm{PO}_{4}\right)\) to a beaker. They then added a constant volume of cobalt(II) nitrate solution \(\left(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\right),\) stirred the contents, and allowed the beakers to sit overnight. The next day, each beaker had a purple precipitate at the bottom. The students decanted the supernatant from each beaker, divided it into two samples, and added one drop of sodium phosphate solution to one sample and one drop of cobalt(II) nitrate solution to the second sample. Their results are shown in Table \(11.5 .\) \begin{equation} \begin{array}{l}{\text { a. Write a balanced chemical equation for the reaction. }} \\ {\text { b. Based on the results, identify the limiting reactant }} \\ {\text { and the excess reactant for each trial. }}\end{array} \end{equation}

Step-by-Step Solution

Answer

Write the balanced equation: \[ 2 \text{Na}_3\text{PO}_4 + 3 \text{Co}\left(\text{NO}_3\right)_2 \rightarrow \text{Co}_3(\text{PO}_4)_2 + 6 \text{NaNO}_3 \]. Determine limiting reactant by observing which addition forms a precipitate in each trial.

Step 1: Writing the Balanced Chemical Equation

The reaction involves sodium phosphate \(\left(\text{Na}_3\text{PO}_4\right)\) and cobalt(II) nitrate \(\left(\text{Co}\left(\text{NO}_3\right)_2\right)\). Cobalt(II) phosphate \(\left(\text{Co}_3(\text{PO}_4)_2\right)\) is formed as a precipitate with sodium nitrate \(\left(\text{NaNO}_3\right)\) as a byproduct. The balanced chemical equation is: \[ 2 \text{Na}_3\text{PO}_4 + 3 \text{Co}\left(\text{NO}_3\right)_2 \rightarrow \text{Co}_3(\text{PO}_4)_2 + 6 \text{NaNO}_3 \]

Step 2: Analyzing the Reaction Results

To determine the limiting and excess reactants, observe what happens when a drop of each reactant is added to the supernatant: 1) If the precipitate forms when sodium phosphate is added, then cobalt(II) nitrate was limiting. 2) If the precipitate forms when cobalt(II) nitrate is added, sodium phosphate was limiting.

Step 3: Identifying Limiting and Excess Reactants for Each Trial

Review the results from Table 11.5 for each trial. For each observation, note which addition caused a precipitate: 1) If a precipitate appears after adding sodium phosphate, cobalt(II) nitrate is the limiting reactant, and sodium phosphate is in excess. 2) If a precipitate appears after adding cobalt(II) nitrate, sodium phosphate is the limiting reactant, and cobalt(II) nitrate is in excess.

Key Concepts

Balanced Chemical Equation

In chemical reactions, a balanced chemical equation is crucial for representing the transformation of reactants into products clearly and accurately. It acts like a recipe, showing the exact proportions of reactants needed to form products without any shortage or leftover.
For the given reaction involving sodium phosphate (\(\text{Na}_3\text{PO}_4\)) and cobalt(II) nitrate (\(\text{Co}\left(\text{NO}_3\right)_2\)), balancing the chemical equation ensures that we follow the law of conservation of mass. This law states that matter cannot be created or destroyed in a chemical reaction.
For example, in the balanced equation:

• 2 units of sodium phosphate react with 3 units of cobalt(II) nitrate.
• This results in the formation of one unit of cobalt(II) phosphate (\(\text{Co}_3(\text{PO}_4)_2\)), which appears as a purple precipitate.
• Additionally, there are 6 units of sodium nitrate (\(\text{NaNO}_3\)) produced.

Balancing each element on both sides of the equation ensures the reaction is depicted accurately. It's vital for predicting the outcome of the reaction and determining the amounts of products formed.

Chemical Reaction Analysis

Conducting a chemical reaction analysis allows us to understand which substances limit the formation of products and which remain in excess. This insight helps us optimize reactions efficiently.
In the exercise mentioned, sodium phosphate and cobalt(II) nitrate were mixed, resulting in a purple precipitate, cobalt(II) phosphate. Observing which substance limits the reaction is key to understanding product formation.
When students added drops of each reactant to the remaining solution, they noted whether more precipitate formed. This helped identify which reactant was fully consumed (limiting) and which was left over (excess).
This analysis is like determining which ingredient in a recipe was insufficient and which was surplus, allowing scientists or students to adjust quantities for optimizing reactions.

Precipitation Formation

Precipitation formation occurs when two solutions react to produce an insoluble solid, known as a precipitate, which settles out of the liquid mixture. This is a common occurrence in reactions involving ionic compounds.
In the students' lab experiment, the reaction between sodium phosphate and cobalt(II) nitrate resulted in the precipitation of cobalt(II) phosphate, a purple solid. This process is driven by the interactions between the ions in the solution, leading to the formation of an insoluble compound.

• As the solutions of reactants are mixed, certain ions attract each other and bind strongly, forming a solid substance that exits the liquid mixture.
• The visible purple precipitate indicates the successful formation of cobalt(II) phosphate, confirming the progress of the reaction.

Precipitation can be a useful indicator that a reaction has occurred, and it's often used in qualitative analysis to help identify unknown substances.

Stoichiometry

Stoichiometry is the mathematical calculation of reactants and products in chemical reactions. It is essential for determining quantities needed or produced in a reaction.
Using stoichiometry, we can predict how much product will form from a given amount of reactants, as in the textbook exercise. The balanced chemical equation acts as a guide in these calculations.

• The coefficients in the balanced equation represent the proportionate amounts of each substance.
• For example, 2 moles of sodium phosphate react with 3 moles of cobalt(II) nitrate to yield one mole of cobalt(II) phosphate and 6 moles of sodium nitrate.
• This allows for calculating the starting amount of reactants required to form a desired quantity of product without wasting materials.

By using stoichiometric principles, students can identify limiting and excess reactants, ensuring efficient use of resources in chemical processes.