Problem 183 - Chemistry Matter and Change

Question

Determine the percent composition of \(\mathrm{MgCO}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and draw a pie graph to represent the hydrate.

Step-by-Step Solution

Answer

MgCO₃ is 48.34% and water is 51.65% of the hydrate MgCO₃·5H₂O.

Step 1: Understand the chemical formula

The chemical formula \( \text{MgCO}_3 \cdot 5 \text{H}_2\text{O} \) represents magnesium carbonate as a hydrate, which includes 5 water molecules for each \( \text{MgCO}_3 \) unit. To solve this problem, we need to determine the molar masses of \( \text{MgCO}_3 \) and \( \text{H}_2\text{O} \).

Step 2: Calculate the molar masses

First, calculate the molar mass of \( \text{MgCO}_3 \):- Mg = 24.31 g/mol- C = 12.01 g/mol- O = 16.00 g/molTherefore, \( \text{MgCO}_3 = 24.31 + 12.01 + (16.00 \times 3) = 84.32 \) g/mol.Next, calculate the molar mass of water, \( \text{H}_2\text{O} \):- H = 1.01 g/mol- O = 16.00 g/molSo, \( \text{H}_2\text{O} = (1.01 \times 2) + 16.00 = 18.02 \) g/mol.

Step 3: Determine the mass of the entire hydrate

Now, calculate the mass of \( \text{MgCO}_3 \cdot 5 \text{H}_2\text{O} \):- \( \text{MgCO}_3 = 84.32 \) g/mol- 5 \( \times \) Mallar mass of \(H_2O = 5 \times 18.02 = 90.10 \) g/molTherefore, the total molar mass is:\[ 84.32 + 90.10 = 174.42 \text{ g/mol} \]

Step 4: Calculate the percent composition

To find the percent composition of each component, use the formula:\[ \text{Percent Composition} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]For \( \text{MgCO}_3 \):\[ \frac{84.32}{174.42} \times 100 \approx 48.34\% \]For the 5 water molecules:\[ \frac{90.10}{174.42} \times 100 \approx 51.65\% \]

Step 5: Draw a Pie Graph

Using the computed percentages, you can create a pie graph. One section represents \( \text{MgCO}_3 \) comprising approximately 48.34% of the hydrate. The other section represents the water component, approximately 51.65%.

Key Concepts

Molar Mass Calculation

The calculation of molar mass is a fundamental step in determining the percent composition of a compound. To begin with, you need to understand that the molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). For the compound magnesium carbonate hydrate \( \text{MgCO}_3 \cdot 5 \text{H}_2\text{O} \), the first task is to calculate the molar mass of its components.
Start by calculating the molar mass of \( \text{MgCO}_3 \):

• Magnesium (\( \text{Mg} \)) has a molar mass of 24.31 g/mol.
• Carbon (\( \text{C} \)) has a molar mass of 12.01 g/mol.
• Oxygen (\( \text{O} \)) has a molar mass of 16.00 g/mol.
• Therefore, \( \text{MgCO}_3 = 24.31 + 12.01 + (16.00 \times 3) = 84.32 \) g/mol.

Next, calculate the molar mass of water \( \text{H}_2\text{O} \):

• Hydrogen (\( \text{H} \)) has a molar mass of 1.01 g/mol.
• Adding oxygen, \( \text{H}_2\text{O} = (1.01 \times 2) + 16.00 = 18.02 \) g/mol.

These calculations allow you to further determine the mass of the entire magnesium carbonate hydrate by considering the amount of water molecules attached.

Hydrate Chemistry

Hydrate chemistry delves into the fascinating realm of compounds composed of water molecules loosely bound within a crystalline structure. In the case of magnesium carbonate hydrate, the notation \( \text{MgCO}_3 \cdot 5 \text{H}_2\text{O} \) indicates that for every molecule of magnesium carbonate, five water molecules are incorporated.
This integration of water molecules can significantly affect the physical properties of the compound including its weight and crystal structure. To visualize this:

• The magnesium carbonate contributes a calculated mass of 84.32 g/mol.
• The five water molecules contribute 90.10 g/mol, making the water the slightly larger fraction in the mass balance.
• The overall molar mass of magnesium carbonate hydrate therefore becomes 174.42 g/mol.

Recognizing these relationships is crucial when evaluating reactions involving hydrates or preparing mixtures where precise mass distribution is essential.

Pie Graph Representation

Creating a visual representation like a pie graph can make the composition of complex compounds easier to understand. By visualizing magnesium carbonate hydrate's composition, we clarify the balance between its constituent parts.
In our percent composition analysis of \( \text{MgCO}_3 \cdot 5 \text{H}_2\text{O} \):

• We found \( \text{MgCO}_3 \) contributes approximately 48.34%.
• Meanwhile, the five water molecules make up about 51.65%.

To draw a pie graph based on these findings, you allocate slightly more than half of the circle to represent the water content, and the remaining portion for magnesium carbonate. This graphical representation not only reinforces the numerical calculations but also provides an intuitive grasp of the hydrate's structure and composition.

Magnesium Carbonate Hydrate

Magnesium carbonate hydrate is a particular form of magnesium carbonate where water is embedded within the crystal lattice. This can dramatically influence various aspects of the compound including its handling, stability, and reactivity.
An understanding of each constituent:

• \( \text{MgCO}_3 \) forms a stable base with a distinct molar mass contributing to various industrial and laboratory applications.
• The \( 5 \text{H}_2\text{O} \) provides additional weight and influences the compound's properties as a hydrate.
• The interaction between these components fits within the broad field of coordination chemistry, where metal ions bond with surrounding molecules including water.

Through such examples, we can observe how simple molecular additions like hydration can extend the utility and manipulation possibilities of basic chemical compounds.