Question

A 1.628-g sample of a hydrate of magnesium iodide is heated until its mass is reduced to 1.072 g and all water has been removed. What is the formula of the hydrate?

Short answer

The formula of the hydrate is MgI2 • 8H2O, which indicates that there are 8 moles of water (H2O) for every mole of magnesium iodide (MgI2) in the hydrate.

Step-by-step solution

Calculate the mass of water lost during heating

To determine the mass of water that was lost during the heating process, we can subtract the mass of the anhydrous sample (after heating) from the mass of the hydrate (before heating): Mass of water = Mass of hydrate - Mass of anhydrous sample Mass of water = 1.628 g - 1.072 g Mass of water = 0.556 g

Calculate the number of moles of anhydrous magnesium iodide and water

We need to find the number of moles of magnesium iodide (MgI2) and water (H2O). For this, we will use the molar masses of these substances. The molar mass of MgI2 is 278.10 g/mol and that of H2O is 18.02 g/mol. Moles of MgI2 = Mass of MgI2 / Molar mass of MgI2 Moles of MgI2 = 1.072 g / 278.10 g/mol Moles of MgI2 = 0.00385 mol Moles of H2O = Mass of H2O / Molar mass of H2O Moles of H2O = 0.556 g / 18.02 g/mol Moles of H2O = 0.0308 mol

Obtain the mole ratio between MgI2 and H2O

To find the formula of the hydrate, we need to determine the ratio between the moles of MgI2 and H2O. We will divide the moles of each substance by the smaller value to obtain a ratio. Mole ratio of MgI2 : H2O = (Moles of MgI2 / Moles of MgI2) : (Moles of H2O / Moles of MgI2) Mole ratio of MgI2 : H2O = (0.00385 mol / 0.00385 mol) : (0.0308 mol / 0.00385 mol) Mole ratio of MgI2 : H2O = 1 : 8

Write the formula of the hydrate

Now that we have the mole ratio between MgI2 and H2O, we can write the formula of the hydrate. The mole ratio of 1 : 8 means that there are 8 moles of water for every mole of MgI2 in the hydrate. Therefore, the formula of the hydrate is: MgI2 • 8H2O

Key concepts

Moles Calculation

In chemistry, the concept of moles is pivotal for substance measurements. The mole is a unit that represents a quantity of substance containing as many entities as there are atoms in 12 grams of pure carbon-12. This number is Avogadro's number, approximately equal to \(6.022 \times 10^{23}\). When calculating moles, you use the relation between the mass of a substance and its molar mass.
Molar mass is important because it allows you to connect mass to moles. To calculate the number of moles from the mass, use the formula:

• \( \text{moles} = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}} \)

In the exercise, moles of magnesium iodide (MgI₂) and water (H₂O) were calculated. You divide the mass of each by their respective molar masses:

• For MgI₂: \( \frac{1.072 \text{ g}}{278.10 \text{ g/mol}} = 0.00385 \text{ mol} \)
• For H₂O: \( \frac{0.556 \text{ g}}{18.02 \text{ g/mol}} = 0.0308 \text{ mol} \)

These calculations allow us to further determine the chemical formula of the hydrate.

Mole Ratio

Understanding the mole ratio is crucial when determining the relationship between different substances in a chemical reaction or compound. The mole ratio is essentially the proportion of moles of one substance to the moles of another substance in a compound or a reaction.
In the context of a hydrate, you need to find out how many mole parts of water are associated with one mole part of the anhydrous compound. This involves dividing the moles of each component by the smallest number of moles calculated.
For instance, in the case of magnesium iodide hydrate, we calculated:

• Moles of MgI₂: 0.00385 mol
• Moles of H₂O: 0.0308 mol

To find the ratio, both values are divided by the smaller number of moles (0.00385 mol for MgI₂):

• For MgI₂: \( \frac{0.00385}{0.00385} = 1\)
• For H₂O: \( \frac{0.0308}{0.00385} \approx 8\)

This mole ratio of 1:8 tells us there are 8 moles of water for every 1 mole of MgI₂.

Water of Crystallization

Water of crystallization plays a significant role in defining the structure and formula of crystalline substances known as hydrates. A hydrate is a chemical compound that contains water molecules within its crystal structure.
The water of crystallization is critical as it contributes significantly to the physical properties of the hydrate, such as its solubility and melting point. During the heating of a hydrate, the water molecules are generally expelled, leaving behind an anhydrous compound.
In the given exercise, by heating the sample of the magnesium iodide hydrate, the water molecules were removed, resulting in a decrease in mass due to the water's loss. By determining the mass of water lost and calculating the moles of water removed, we can effectively determine how many water molecules were originally present in the hydrated compound.

• For example, after heating, the loss of water from the hydrate sample allowed us to find the ratio of water to magnesium iodide as 8:1.

The chemical formula, MgI₂ • 8H₂O, reveals that each formula unit of MgI₂ integrates 8 water molecules into its crystalline framework.