Problem 79 - Chemistry Matter and Change

Question

Apply A hydrate contains 0.050 mol of \(\mathrm{H}_{2} \mathrm{O}\) to every 0.00998 mol of ionic compound. Write a generalized formula of the hydrate.

Step-by-Step Solution

Answer

The generalized formula for the hydrate, given a mole ratio of 0.050 mol \(\mathrm{H}_{2} \mathrm{O}\) to 0.00998 mol ionic compound, is: Ionic compound · 5H2O.

Step 1: Calculate the mole ratio between water and ionic compound

Given 0.050 moles of \(\mathrm{H}_{2} \mathrm{O}\) and 0.00998 moles of ionic compound, we can calculate the mole ratio by dividing both values by the smaller value (0.00998 moles): \[ \frac{0.050 \ \cancel{\text{moles }}\mathrm{H_2O}}{0.00998 \ \cancel{\text{moles ionic compound}}} = 5.010 \]

Step 2: Round the ratio to the nearest whole number

Since the mole ratio indicates the relative number of moles for every \(\mathrm{H}_{2} \mathrm{O}\) and the ionic compound, it should be a whole number. In this case, we can round the number to the nearest whole number to obtain a close approximation: \[ 5.010 \approx 5 \]

Step 3: Write the general formula for the hydrate

Now that we have the mole ratio (5:1) between water and the ionic compound, we can write the generalized formula for the hydrate using the notation "nH2O" for the number of water molecules: Ionic compound · 5H2O This is the generalized formula for the hydrate with the given ratio of moles of \(\mathrm{H}_{2} \mathrm{O}\) and ionic compound.

Key Concepts

Mole Ratio Calculation

When handling hydrates in chemistry, calculating the mole ratio is vital. It helps to determine the number of water molecules attached to each unit of an ionic compound in a hydrate. To find this ratio:

• Identify the moles of water (for example, \(0.050\) mol of \(\mathrm{H}_2\mathrm{O}\)).
• Identify the moles of the ionic compound (for example, 0.00998 mol).
• Divide the number of moles of water by the moles of ionic compound.

In our scenario, divide \(0.050\) by \(0.00998\), which gives approximately 5.010.
To make it simple in formulas, we often round off to the nearest whole number, since you can't have a fraction of a water molecule attached. After rounding, the ratio is 5:1.
This means that for every part of the ionic compound, there are roughly 5 parts water molecules attached.

Ionic Compounds

Ionic compounds are formed when metals transfer electrons to non-metals, resulting in a strong bond due to opposite charges. This transfer leads to a unique set of properties, including:

• High melting and boiling points due to strong ionic bonds.
• They are generally soluble in water.
• They conduct electricity when dissolved in water or melted, because the ions are free to move.

In hydrates, these ionic compounds have water molecules embedded in their structure. These water molecules are not forming new chemicals, but they are part of the solid's structure, affecting the consistency and weight of the compound.
Understanding ionic compounds in the context of hydrates helps in grasping why these strong, ionically bonded structures hold water within their crystal lattice.

General Formula for Hydrates

The general formula for hydrates is used to represent compounds that include a specific number of water molecules associated with each unit of the compound. It's typically expressed as:
\[ \text{Ionic Compound} \cdot n \mathrm{H}_2\mathrm{O} \]Where \(n\) represents the mole ratio of water to the ionic compound.
This standardized means of notation ensures clarity in how hydrates are composed.
For example, if a hydrate has a 5:1 mole ratio (as calculated above), the formula would be "Ionic Compound · 5H2O". This means that for every 1 unit of the ionic compound, there are 5 water molecules associated.
Hydrates are more than just a formula—they signify the importance of water in the stability and characteristics of a compound. The formula helps chemists to communicate the composition efficiently, ensuring accurate replication in experiments and clarity in chemical equations.