Question

A hydrated iron chloride compound was found to contain \(20.66 \% \mathrm{Fe}, 39.35 \% \mathrm{Cl}\), and \(39.99 \%\) water. Determine the empirical formula of this hydrated compound.

Short answer

The empirical formula is \( \text{FeCl}_3 \cdot 6 \text{H}_2\text{O} \).

Step-by-step solution

- Convert percentages to grams

Assume you have 100 grams of the compound. This means you have 20.66 grams of Fe, 39.35 grams of Cl, and 39.99 grams of water.

- Convert grams to moles

Use the molar masses to convert grams to moles: Fe: \( \frac{20.66 \text{ grams}}{55.85 \text{ g/mol}} = 0.37 \text{ moles} \) Cl: \( \frac{39.35 \text{ grams}}{35.45 \text{ g/mol}} = 1.11 \text{ moles} \) H2O: \( \frac{39.99 \text{ grams}}{18.015 \text{ g/mol}} = 2.22 \text{ moles} \)

- Determine mole ratio

Divide each mole value by the smallest number of moles from Step 2. Fe: \( \frac{0.37}{0.37} = 1 \) Cl: \( \frac{1.11}{0.37} = 3 \) H2O: \( \frac{2.22}{0.37} = 6 \)

- Write the empirical formula

Using the mole ratio from Step 3, the empirical formula of the compound is \( \text{FeCl}_3 \cdot 6 \text{H}_2\text{O} \).

Key concepts

hydrated compound analysis

Hydrated compounds are substances that include water molecules within their crystal structure. These water molecules are not just trapped inside but are chemically bonded to the compound. To determine the composition of such compounds, we have to identify and analyze both the anhydrous part and the water molecules.

When analyzing a hydrated compound, the steps generally involve:

• Identifying the percentage of each component including water.
• Converting these percentages to grams for easier calculations.
• Using molar masses to convert these grams into moles.
• Determining the ratio of moles to establish the empirical formula.
  

It's essential to correctly distinguish between the water of crystallization and the rest of the compound, as this dictates the nature and properties of the substance.

In this example, the hydrated iron chloride contains water, making it a specific type of compound known as a hydrate. An analysis like this ensures a complete understanding of its formula and properties.

mole ratio calculation

The mole ratio is a fundamental concept in chemistry that helps in determining how different elements combine to form compounds. Essentially, it tells you the proportion of each element in a compound.
To calculate the mole ratio, we first convert the mass of each component into moles using their respective molar masses. These steps help us achieve that:

• First, convert the given mass percentages to grams by assuming you have exactly 100 grams of the compound as it simplifies calculations.
• Next, convert the mass of each element to moles by dividing by its molar mass. For instance, in the example:
  Fe: \( \frac{20.66 g}{55.85 g/mol} = 0.37 moles \)
  Cl: \( \frac{39.35 g}{35.45 g/mol} = 1.11 moles \)
  H\textsubscript{2}O: \( \frac{39.99 g}{18.015 g/mol} = 2.22 moles \)
  
• Finally, divide each mole value by the smallest number of moles calculated to find the simplest whole number ratio.
  Using the example, we divided by 0.37 (smallest moles value):
  Fe: \( \frac{0.37}{0.37} = 1 \)
  Cl: \( \frac{1.11}{0.37} \approx 3 \)
  H\textsubscript{2}O: \( \frac{2.22}{0.37} \approx 6 \)
  

With these ratios, you can determine the empirical formula. In this case, \text{FeCl}\textsubscript{3}\text{·6H}\textsubscript{2}\text{O} is the resulting empirical formula from the calculated ratios.

molar mass conversion

Molar mass conversion is crucial in chemistry for converting between grams and moles. This allows chemists to measure substances accurately and understand their composition. Each element has a molar mass, typically found on the periodic table, representing the mass of one mole of that element.

Here's how to convert grams to moles in a few steps:

• Identify the molar mass of the element or compound. For instance, in our example:
• Fe has a molar mass of 55.85 g/mol,
• Cl has a molar mass of 35.45 g/mol,
• and H\textsubscript{2}O has a molar mass of 18.015 g/mol.
• Use the formula: \( \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} \).
• Apply this formula to each component to convert their mass to moles. In our exercise example, it was done as follows:
• Fe: \( \frac{20.66 \text{ grams}}{55.85 \text{ g/mol}} = 0.37 \text{ moles} \),
• Cl: \( \frac{39.35 \text{ grams}}{35.45 \text{ g/mol}} = 1.11 \),
• H\textsubscript{2}O: \( \frac{39.99 \text{ grams}}{18.015 \),

Once you have the moles, they can be used to find the mole ratio or to calculate the empirical formula, which gives you a clearer picture of the compound's composition.
Properly understanding and using molar masses is essential for any accurate chemical analysis or reaction preparation.