Problem 57 - Chemistry and Chemical Reactivity

Question

If Epsom salt, \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},\) is heated to \(250^{\circ} \mathrm{C},\) all the water of hydration is lost. On heating a 1.687 -g sample of the hydrate, \(0.824 \mathrm{g}\) of \(\mathrm{MgSO}_{4}\) remains. How many molecules of water occur per formula unit of \(\mathrm{MgSO}_{4} ?\)

Step-by-Step Solution

Answer

The formula unit contains 7 molecules of water.

Step 1: Determine the Mass of Water Lost

To find the mass of water that was lost upon heating, subtract the mass of anhydrous magnesium sulfate (\(0.824 \text{ g}\)) from the mass of the hydrate sample (\(1.687 \text{ g}\)).\[\text{Mass of water lost} = 1.687 \text{ g} - 0.824 \text{ g} = 0.863 \text{ g}\]

Step 2: Calculate Moles of Anhydrous \(\mathrm{MgSO}_4\)

Use the molar mass of \(\mathrm{MgSO}_4\) to determine the number of moles present in \(0.824 \text{ g}\). The molar mass of \(\mathrm{MgSO}_4\) is approximately \(120.37 \text{ g/mol}\).\[\text{Moles of } \mathrm{MgSO}_4 = \frac{0.824 \text{ g}}{120.37 \text{ g/mol}} \approx 0.00684 \text{ mol}\]

Step 3: Calculate Moles of Water Lost

The molar mass of water (\(\mathrm{H}_2\mathrm{O}\)) is \(18.015 \text{ g/mol}\). Calculate the number of moles of water in \(0.863 \text{ g}\) of water.\[\text{Moles of water} = \frac{0.863 \text{ g}}{18.015 \text{ g/mol}} \approx 0.0479 \text{ mol}\]

Step 4: Find Hydration Number (Number of Water Molecules per Formula Unit)

Calculate the number of water molecules per formula unit of \(\mathrm{MgSO}_4\) by dividing the moles of water by the moles of \(\mathrm{MgSO}_4\).\[x = \frac{0.0479 \text{ mol water}}{0.00684 \text{ mol } \mathrm{MgSO}_4} \approx 7\]Thus, there are approximately 7 molecules of water per formula unit of \(\mathrm{MgSO}_4\).

Key Concepts

Epsom Salt

Epsom salt is a versatile compound used in many applications, from gardening to bathing. Chemically, it is known as magnesium sulfate (\(\mathrm{MgSO}_4\)). Epsom salt is unique because it naturally occurs as a hydrate, which means it contains water molecules within its crystal structure. This is referred to as water of hydration. When expressed chemically, Epsom salt is often written as \(\mathrm{MgSO}_4 \cdot x \mathrm{H}_2 \mathrm{O}\).

• The "\(x\)" in the formula represents the number of water molecules present.
• Upon heating, these water molecules are released, leaving behind an anhydrous form of the salt.

Understanding how many water molecules are present is crucial for determining the properties and applications of the salt.

Moles Calculation

Moles calculation is a fundamental skill in chemistry, as it allows you to determine the number of particles, such as atoms or molecules, involved in a chemical reaction or present in a sample. In this context, we use moles calculation to determine the amount of substances in Epsom salt before and after heating. To calculate moles:

• Use the formula: \(\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\)
• The molar mass is the weight of one mole of a substance. For example, the molar mass of \(\mathrm{MgSO}_4\) is approximately 120.37 g/mol, which we used to calculate the moles of the anhydrous compound.

Knowing how to calculate moles helps in finding out how much of each substance is involved in a chemical change.

Water of Hydration

Water of hydration refers to the water molecules that are part of the crystalline structure of a hydrate. These molecules are not just physically mixed with the compound but are integral in forming its structure.

• When a hydrate like Epsom salt is heated, the water of hydration is evaporated, leaving the anhydrous form.
• In our example, the mass loss upon heating indicates the amount of water initially present.
• By calculating the mass difference, we determined how much water was in the original sample.

This is critical when predicting how a substance will behave under different conditions, such as heat.

Anhydrous Compound

An anhydrous compound is one that does not contain water, either as part of its structure or mixed in. The term "anhydrous" comes from the Greek word "an," meaning "without," and "hydor," meaning "water."Once the hydrate is heated and loses its water of hydration, it turns into its anhydrous form. For magnesium sulfate, this means transforming from \(\mathrm{MgSO}_4 \cdot 7\mathrm{H}_2 \mathrm{O}\) (hydrated) to \(\mathrm{MgSO}_4\) (anhydrous).

• Anhydrous compounds are often more stable for storage and use.
• They offer a way to make precise calculations in reactions where water would hinder progress.

Understanding the difference between anhydrous and hydrated forms is crucial in many scientific and industrial applications.