An excess of `NaOH` was added to `100 mL` of a `FeCl_(3)` solution which gives `2.14g` of `Fe (OH)_(3)`. Calculate the molarity of `FeCl_(3)` solution.

Options

A. 0.3 M
B. 0.2 M
C. 0.6 M
D. 1.8 M

Answer

To solve the question, we need to determine the molarity of the FeCl₃ solution based on the amount of Fe(OH)₃ produced when NaOH is added. Here’s a step-by-step breakdown of the solution:

### Step 1: Write the Balanced Chemical Equation
The reaction between NaOH and FeCl₃ can be represented as follows:

\[ \text{FeCl}_3 + 3 \text{NaOH} \rightarrow \text{Fe(OH)}_3 + 3 \text{NaCl} \]

This equation shows that one mole of FeCl₃ reacts with three moles of NaOH to produce one mole of Fe(OH)₃.

### Step 2: Calculate the Molar Mass of Fe(OH)₃
To find the number of moles of Fe(OH)₃ produced, we first need to calculate its molar mass.

- Molar mass of Fe = 56 g/mol
- Molar mass of O = 16 g/mol
- Molar mass of H = 1 g/mol

The molar mass of Fe(OH)₃ is calculated as follows:

\[ \text{Molar mass of Fe(OH)}_3 = 56 + 3 \times (16 + 1) = 56 + 3 \times 17 = 56 + 51 = 107 \text{ g/mol} \]

### Step 3: Calculate the Number of Moles of Fe(OH)₃
Given that 2.14 g of Fe(OH)₃ is produced, we can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Substituting the known values:

\[ \text{Number of moles of Fe(OH)}_3 = \frac{2.14 \text{ g}}{107 \text{ g/mol}} \approx 0.0200 \text{ moles} \]

### Step 4: Determine the Moles of FeCl₃
From the balanced equation, we see that 1 mole of FeCl₃ produces 1 mole of Fe(OH)₃. Therefore, the number of moles of FeCl₃ is equal to the number of moles of Fe(OH)₃ produced:

\[ \text{Moles of FeCl}_3 = 0.0200 \text{ moles} \]

### Step 5: Calculate the Molarity of FeCl₃
Molarity (M) is defined as the number of moles of solute per liter of solution. The volume of the FeCl₃ solution is given as 100 mL, which we convert to liters:

\[ \text{Volume in liters} = \frac{100 \text{ mL}}{1000} = 0.1 \text{ L} \]

Now, we can calculate the molarity:

\[ \text{Molarity of FeCl}_3 = \frac{\text{Number of moles of FeCl}_3}{\text{Volume in liters}} = \frac{0.0200 \text{ moles}}{0.1 \text{ L}} = 0.200 \text{ M} \]

### Final Answer
The molarity of the FeCl₃ solution is **0.2 M**.

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