A hydrate of iron (III) thiocynate `Fe(SCN)_(3)`, was found to contain `19% H_(2)O`. What is the formula of the hydrate?

Options

A. `Fe(SCN)_3. H_2O`
B. `Fe(SCN)_3. 2H_2O`
C. `Fe (SCN)_3. 3 H_2O`
D. `Fe(SCN)_3. 4H_2O`

Answer

To determine the formula of the hydrate of iron (III) thiocyanate, \( Fe(SCN)_3 \), which contains 19% water, we can follow these steps:

### Step 1: Assume the formula of the hydrate
Let the formula of the hydrate be \( Fe(SCN)_3 \cdot nH_2O \), where \( n \) is the number of moles of water.

### Step 2: Calculate the molar mass of \( Fe(SCN)_3 \)
To find the molar mass of \( Fe(SCN)_3 \):
- Atomic mass of Iron (Fe) = 56 g/mol
- Atomic mass of Sulfur (S) = 32 g/mol
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Nitrogen (N) = 14 g/mol

The formula \( SCN \) consists of:
- 1 Sulfur (S)
- 1 Carbon (C)
- 1 Nitrogen (N)

Thus, the molar mass of \( SCN \) is:
\[ M(SCN) = 32 + 12 + 14 = 58 \text{ g/mol} \]
Since there are 3 thiocyanate ions in the formula, the total mass contributed by \( SCN \) is:
\[ 3 \times 58 = 174 \text{ g/mol} \]
Adding the mass of Iron:
\[ M(Fe(SCN)_3) = 56 + 174 = 230 \text{ g/mol} \]

### Step 3: Calculate the mass of water in the hydrate
The mass of water in the hydrate can be expressed as:
\[ \text{Mass of water} = 18n \text{ g/mol} \quad (\text{since } M(H_2O) = 18 \text{ g/mol}) \]

### Step 4: Set up the equation using the percentage of water
According to the problem, the percentage of water in the hydrate is given as 19%. Therefore, we can set up the equation:
\[ \frac{18n}{230 + 18n} \times 100 = 19 \]

### Step 5: Solve for \( n \)
Rearranging the equation:
\[ \frac{18n}{230 + 18n} = 0.19 \]
Cross-multiplying gives:
\[ 18n = 0.19(230 + 18n) \]
Expanding the right side:
\[ 18n = 43.7 + 3.42n \]
Now, isolate \( n \):
\[ 18n - 3.42n = 43.7 \]
\[ 14.58n = 43.7 \]
\[ n = \frac{43.7}{14.58} \approx 3 \]

### Step 6: Write the final formula of the hydrate
Now that we have \( n = 3 \), the formula of the hydrate is:
\[ Fe(SCN)_3 \cdot 3H_2O \]

### Final Answer:
The formula of the hydrate is \( Fe(SCN)_3 \cdot 3H_2O \).

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