Problem 31 - Chemistry and Chemical Reactivity

Question

A mixture of \(\mathrm{CuSO}_{4}\) and \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has a mass of 1.245 g. After heating to drive off all the water, the mass is only \(0.832 \mathrm{g} .\) What is the mass percent of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture? (See page \(129 .\) )

Step-by-Step Solution

Answer

The mass percent of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) in the mixture is approximately 91.56%.

Step 1: Understanding the problem

We have a mixture of anhydrous copper sulfate \((\text{CuSO}_4)\) and hydrated copper sulfate \((\text{CuSO}_4 \cdot 5 \text{H}_2\text{O})\). The total mass of the mixture is given as 1.245 g. After heating, only the anhydrous copper sulfate remains, weighing 0.832 g. We need to find the mass percent of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) in the mixture.

Step 2: Calculate mass of water lost

To find the mass of water lost upon heating, subtract the mass of anhydrous copper sulfate from the original mass of the mixture: \\[ 1.245 \text{ g} - 0.832 \text{ g} = 0.413 \text{ g (mass of water driven off)} \]

Step 3: Calculate mass of hydrated copper sulfate

The mass of water lost corresponds to the water in the hydrated copper sulfate. Let's calculate the mass of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\):\1 mole of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) loses 5 moles of water upon heating. The molar mass of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) is approximately 249.5 g/mol.Now, we set up a proportion:\[ \left( \text{Mass of } \text{CuSO}_4 \cdot 5 \text{H}_2\text{O} \right) \times \frac{90.0}{249.5} = 0.413 \text{ g} \] Solve for the mass of hydrated copper sulfate:\[ \text{Mass of } \text{CuSO}_4 \cdot 5 \text{H}_2\text{O} = \frac{0.413 \times 249.5}{90} \approx 1.14 \text{ g} \]

Step 4: Calculate mass percent of hydrated copper sulfate

We have the mass of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) calculated as 1.14 g. Now, find the mass percent in the mixture:\[ \text{Mass percent of } \text{CuSO}_4 \cdot 5 \text{H}_2\text{O} = \left( \frac{1.14}{1.245} \right) \times 100 \% \approx 91.56 \% \]

Key Concepts

Mass Percent Calculation

Calculating mass percent is a way to figure out the percentage of a particular component within a mixture. In this case, we're focusing on hydrated copper sulfate, \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\), in a given mixture. To calculate mass percent, you divide the mass of the component by the total mass of the mixture and multiply by 100.
For example, once we determined that the mass of hydrated copper sulfate was 1.14 grams, we divided this by the total mass of the mixture (1.245 grams) and then multiplied by 100 to get the percentage.

• Mass Percent Formula: \(\left(\frac{\text{mass of component}}{\text{total mass of mixture}}\right) \times 100\%\)
• In our scenario: \(\left(\frac{1.14}{1.245}\right) \times 100 \approx 91.56\%\)

Understanding this concept is crucial in chemistry as it helps in analyzing the composition of mixtures.

Anhydrous Copper Sulfate

Anhydrous copper sulfate, \(\text{CuSO}_4\), is a form of copper sulfate that does not contain water.
When hydrated copper sulfate, \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\), is heated, it loses water, turning into the anhydrous form. This transformation is key to understanding the mixture problem you faced.

• Hydrated Form: Contains water molecules, appears crystalline and blue.
• Anhydrous Form: Doesn’t contain water, appears powdery and white.
• The transition involves driving off water through heating, only leaving the \(\text{CuSO}_4\).

In our exercise, we identified the mass of the anhydrous form after heating, allowing us to calculate how much water was lost and in turn, determine the amount of hydrated copper sulfate originally present.

Stoichiometry

Stoichiometry involves using balanced equations to determine the quantities of reactants and products in a chemical reaction.
In our exercise with copper sulfate, stoichiometry guides the calculation of how much water was part of the original hydrated form. Knowing that each molecule of \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) loses exactly 5 water molecules upon heating provides the foundation for our calculations.

• Molar Masses: \(\text{CuSO}_4 \cdot 5 \text{H}_2\text{O}\) is approximately 249.5 g/mol; water is 18 g/mol.
• We calculated the mass of water by realizing 1 mole of hydrate loses 5 moles of water.
• From the water mass lost (0.413 g), we used stoichiometry to determine the original mass of hydrated copper sulfate (1.14 g).

Understanding stoichiometry is vital for converting between the mass of compounds in a reaction, providing accurate insights into the composition and changes in mixtures.