4 g of a hydrated crystal of formula `A.xH_(2)O` has 0.8 g of water. If the molar mass of the anhydrous crystal (A) is `144 g mol^(-1)` The value of x is

Options

A. 4
B. 1
C. 2
D. 3

Explanation

To find the value of \( x \) in the hydrated crystal formula \( A \cdot xH_2O \), we can follow these steps:

### Step 1: Determine the mass of the anhydrous crystal
Given:
- Mass of hydrated crystal = 4 g
- Mass of water = 0.8 g

To find the mass of the anhydrous crystal (A), we subtract the mass of water from the mass of the hydrated crystal:

\[ \text{Mass of anhydrous crystal (A)} = \text{Mass of hydrated crystal} - \text{Mass of water} \]

\[ \text{Mass of A} = 4 \, \text{g} - 0.8 \, \text{g} = 3.2 \, \text{g} \]

### Step 2: Calculate the moles of the anhydrous crystal
We know the molar mass of the anhydrous crystal \( A \) is \( 144 \, \text{g/mol} \).

To find the number of moles of the anhydrous crystal, we use the formula:

\[ \text{Moles of A} = \frac{\text{Mass of A}}{\text{Molar mass of A}} = \frac{3.2 \, \text{g}}{144 \, \text{g/mol}} \]

Calculating this gives:

\[ \text{Moles of A} = \frac{3.2}{144} = 0.0222 \, \text{mol} \]

### Step 3: Calculate the moles of water
The mass of water is given as \( 0.8 \, \text{g} \). The molar mass of water \( H_2O \) is \( 18 \, \text{g/mol} \).

To find the number of moles of water, we use the formula:

\[ \text{Moles of } H_2O = \frac{\text{Mass of } H_2O}{\text{Molar mass of } H_2O} = \frac{0.8 \, \text{g}}{18 \, \text{g/mol}} \]

Calculating this gives:

\[ \text{Moles of } H_2O = \frac{0.8}{18} = 0.0444 \, \text{mol} \]

### Step 4: Find the ratio of moles of water to moles of anhydrous crystal
Now, we can find the value of \( x \) by taking the ratio of the moles of water to the moles of the anhydrous crystal:

\[ x = \frac{\text{Moles of } H_2O}{\text{Moles of A}} = \frac{0.0444}{0.0222} = 2 \]

### Conclusion
Thus, the value of \( x \) is \( 2 \).

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