Problem 81 - Chemistry Matter and Change

Question

Arrange these hydrates in order of increasing percent water content: \(\operatorname{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}, \mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

Order is: CoCl₂ · 6H₂O < Ba(OH)₂ · 8H₂O < MgSO₄ · 7H₂O.

Step 1: Calculate molar mass of each hydrate

First, we will determine the molar mass of each hydrate. **For MgSO₄ · 7H₂O**: Mg: 24.31 g/mol, S: 32.07 g/mol, O: 4 * 16.00 g/mol, 7H₂O: 7 * (2 * 1.01 + 16.00) g/mol Molar mass = 24.31 + 32.07 + 64.00 + 126.14 = 246.52 g/mol **For Ba(OH)₂ · 8H₂O**: Ba: 137.33 g/mol, O: 2 * 16.00 g/mol, H: 2 * 1.01 g/mol, 8H₂O: 8 * (2 * 1.01 + 16.00) g/mol Molar mass = 137.33 + 32.02 + 144.16 = 313.51 g/mol **For CoCl₂ · 6H₂O**: Co: 58.93 g/mol, Cl: 2 * 35.45 g/mol, 6H₂O: 6 * (2 * 1.01 + 16.00) g/mol Molar mass = 58.93 + 70.90 + 108.12 = 237.95 g/mol.

Step 2: Calculate mass of water in each hydrate

Next, calculate the total mass of water for each hydrate. **MgSO₄ · 7H₂O**: Water mass = 7 * (2 * 1.01 + 16.00) = 126.14 g/mol **Ba(OH)₂ · 8H₂O**: Water mass = 8 * (2 * 1.01 + 16.00) = 144.16 g/mol **CoCl₂ · 6H₂O**: Water mass = 6 * (2 * 1.01 + 16.00) = 108.12 g/mol.

Step 3: Calculate percent water content in each hydrate

Now, we will find the percent water content by dividing the mass of water by the total molar mass and multiplying by 100.\(\text{For MgSO₄ · 7H₂O:}\\frac{126.14}{246.52} imes 100 \approx 51.17\%\)\(\text{For Ba(OH)₂ · 8H₂O:}\\frac{144.16}{313.51} imes 100 \approx 45.97\%\)\(\text{For CoCl₂ · 6H₂O:}\\frac{108.12}{237.95} imes 100 \approx 45.43\%\)

Step 4: Compare and order the hydrates by percent water content

Based on the calculated percent water content: - CoCl₂ · 6H₂O has 45.43% water. - Ba(OH)₂ · 8H₂O has 45.97% water. - MgSO₄ · 7H₂O has 51.17% water. Thus, the order of increasing percent water content is: CoCl₂ · 6H₂O < Ba(OH)₂ · 8H₂O < MgSO₄ · 7H₂O.

Key Concepts

Hydrate Chemistry

Hydrates in chemistry are compounds that incorporate water molecules into their crystalline structure. These water molecules are typically in a fixed ratio with the host compound. Each specific hydrate has a particular number of water molecules accompanying one formula unit of the compound.

The water is present in a solid form, creating what is known as "water of crystallization." It's important to note that these water molecules are not just trapped in the structure; they play a crucial role in maintaining the integrity of the crystalline form. A common example of a hydrate includes \( \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \), also known as Epsom salt, which contains seven water molecules per formula unit of magnesium sulfate.

When hydrates are heated, they typically lose their water content, transforming into an anhydrous form. This change can affect their physical and chemical properties significantly. Understanding hydrates is key in processes such as desiccation, where water molecules need to be removed for drying purposes.

Molar Mass Calculation

Calculating molar mass is a fundamental step in assessing various chemical properties, including percent composition. Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol).

The process of calculating the molar mass requires summing the atomic mass units (amu) of all atoms in a chemical formula. For example:

• For \( \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \):\ You add the atomic masses of magnesium (24.31 g/mol), sulfur (32.07 g/mol), oxygen from the sulfate ion, and the added water molecules. \( \text{Molar mass} = 24.31 + 32.07 + 4 \times 16.00 + 7 \times (2 \times 1.01 + 16.00) = 246.52 \text{ g/mol} \)

The calculated molar mass is pivotal in other calculations too, as it helps establish the proportion between different elements in a compound, thus linking it to concepts like percent composition.

Percent Composition

Percent composition indicates the percentage of each constituent element in a compound. In hydrates, a common task is to determine the percentage of water in the compound, or its percent composition by mass.

To calculate percent composition, especially for water in hydrates, use the formula: \ \text{Percent Water} = \left( \frac{\text{Mass of Water}}{\text{Total Molar Mass of Hydrate}} \right) \times 100 \

Let's apply this to our example hydrates:

• For \( \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \):\ \( \frac{126.14}{246.52} \times 100 \approx 51.17\% \)
• For \( \mathrm{Ba(OH)}_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O} \):\ \( \frac{144.16}{313.51} \times 100 \approx 45.97\% \)
• For \( \mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} \):\ \( \frac{108.12}{237.95} \times 100 \approx 45.43\% \)

Percent composition is crucial for chemical analysis and comparing the properties of different hydrates.

Chemical Formulas

Chemical formulas are symbolic representations of chemical compounds. They display the elements present in a compound and their relative numbers.

For instance, the chemical formula for a hydrate like \( \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \) communicates that the compound consists of one magnesium, one sulfur, four oxygen atoms from \( \mathrm{SO}_{4} \), and additional seven water molecules.

• "\( \cdot \)" symbol: This dot between the compound and water molecules signifies that the water is structurally integrated into the crystalline nature of the compound.

Understanding chemical formulas is vital as it serves as a blueprint for calculating other chemical metrics, like molar mass and percent composition. Additionally, chemical formulas can help predict reactions the compound may undergo, especially in processes like thermal decomposition or hydration.