Problem 159
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
Verified Answer
The Epsom salt contains 7 water molecules per formula unit of \(\mathrm{MgSO}_4\).
1Step 1: Calculate the Mass of Water Lost
First, find out how much water was lost when the Epsom salt was heated. Subtract the mass of the anhydrous \( \text{MgSO}_4 \) (0.824 g) from the total mass of the hydrate (1.687 g). \[\text{Mass of water lost} = 1.687 \, \text{g} - 0.824 \, \text{g} = 0.863 \, \text{g}\]
2Step 2: Calculate the Moles of Anhydrous MgSO4
Determine the number of moles of anhydrous \( \text{MgSO}_4 \) using its molar mass, which is approximately 120.38 g/mol.\[\text{Moles of } \text{MgSO}_4 = \frac{0.824 \, \text{g}}{120.38 \, \text{g/mol}} \approx 0.00684 \, \text{mol}\]
3Step 3: Calculate the Moles of Water Lost
Find the number of moles of water that were lost. Use the molar mass of water (approximately 18.015 g/mol).\[\text{Moles of } \text{H}_2\text{O} = \frac{0.863 \, \text{g}}{18.015 \, \text{g/mol}} \approx 0.0479 \, \text{mol}\]
4Step 4: Determine the Water Molecule to Formula Unit Ratio
Find the ratio of moles of water to moles of \( \text{MgSO}_4 \) to determine \( x \), the number of water molecules per formula unit.\[x = \frac{0.0479 \, \text{mol } \text{H}_2\text{O}}{0.00684 \, \text{mol } \text{MgSO}_4} \approx 7\]
5Step 5: Conclusion
The number of water molecules per formula unit of \( \text{MgSO}_4 \) in the hydrate is 7, making the formula \( \text{MgSO}_4 \cdot 7 \text{H}_2\text{O} \).
Key Concepts
HydrationMolar MassMoles CalculationChemical FormulaThermal Decomposition
Hydration
Hydration in chemistry refers to the process where water molecules are absorbed by or associated with other substances. This can result in a compound containing water molecules within its crystalline structure, known as a hydrate.
Epsom salt, scientifically known as magnesium sulfate heptahydrate \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\), is an example of a hydrated compound. Here, seven water molecules are integrated into each formula unit.
These water molecules can typically be removed through heating, which results in a transition from the hydrated to the anhydrous form – where the compound no longer contains water molecules.
This reaction is crucial in determining the number of water molecules initially present in the structure.
Epsom salt, scientifically known as magnesium sulfate heptahydrate \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\), is an example of a hydrated compound. Here, seven water molecules are integrated into each formula unit.
These water molecules can typically be removed through heating, which results in a transition from the hydrated to the anhydrous form – where the compound no longer contains water molecules.
This reaction is crucial in determining the number of water molecules initially present in the structure.
Molar Mass
Molar mass represents the mass of one mole of a substance, measured in grams per mole (g/mol). It is a vital link between the mass of a substance and the number of molecules or atoms it contains.
For instance, the molar mass of anhydrous \(\mathrm{MgSO}_{4}\) is approximately 120.38 g/mol, while the molar mass of water (\(\mathrm{H}_2\mathrm{O}\)) is approximately 18.015 g/mol.
Knowing the molar mass allows conversion between mass and moles, enabling stoichiometric calculations - which are essential in solving problems about chemical reactions and formulas.
For instance, the molar mass of anhydrous \(\mathrm{MgSO}_{4}\) is approximately 120.38 g/mol, while the molar mass of water (\(\mathrm{H}_2\mathrm{O}\)) is approximately 18.015 g/mol.
Knowing the molar mass allows conversion between mass and moles, enabling stoichiometric calculations - which are essential in solving problems about chemical reactions and formulas.
Moles Calculation
Moles calculation is a fundamental aspect of stoichiometry, allowing us to translate between mass and the number of particles in a substance.
To calculate moles, use the formula \(\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\).
For example, when you have 0.824 g of anhydrous \(\mathrm{MgSO}_{4}\) and its molar mass is 120.38 g/mol, the calculation will show approximately 0.00684 moles.
This process applies equally to any substance: divide the mass by its molar mass to find the number of moles.
To calculate moles, use the formula \(\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\).
For example, when you have 0.824 g of anhydrous \(\mathrm{MgSO}_{4}\) and its molar mass is 120.38 g/mol, the calculation will show approximately 0.00684 moles.
This process applies equally to any substance: divide the mass by its molar mass to find the number of moles.
Chemical Formula
A chemical formula reveals the elements present in a compound and the ratios of atoms or ions in that compound. It’s like a recipe that indicates how atoms are grouped together.
In hydrates like Epsom salt (\(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\)), the formula shows that each magnesium sulfate unit is associated with seven water molecules.
Understanding how to read chemical formulas and deduce ratios is crucial, particularly in hydration reactions where the number of associating water molecules impacts the resulting compound’s properties.
In hydrates like Epsom salt (\(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\)), the formula shows that each magnesium sulfate unit is associated with seven water molecules.
Understanding how to read chemical formulas and deduce ratios is crucial, particularly in hydration reactions where the number of associating water molecules impacts the resulting compound’s properties.
Thermal Decomposition
Thermal decomposition involves breaking down a compound into simpler substances through the application of heat.
In the case of Epsom salts, heating causes the water of hydration to be released from the compound, transforming it from \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\) into just \(\mathrm{MgSO}_{4}\).
Understanding thermal decomposition is important in determining the true molecular formula of a hydrate by observing the mass change before and after heating, and identifying the number of water molecules initially present.
In the case of Epsom salts, heating causes the water of hydration to be released from the compound, transforming it from \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2}\) into just \(\mathrm{MgSO}_{4}\).
Understanding thermal decomposition is important in determining the true molecular formula of a hydrate by observing the mass change before and after heating, and identifying the number of water molecules initially present.
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