1.61gm of anhydrous `ZnSO_(4)` was placed in moist air after few days its weight was found to be 2.87 gm. What is the molecular formular by hydrated salt? [Zn = 65]

Options

A. `ZnSO_(4). H_(2)O`
B. `ZnSO_(4). 3H_(2)O`
C. `ZnSO_(4).7H_(2)O`
D. `ZnSO_(4).10H_(2)O`

Answer

To find the molecular formula of the hydrated salt formed from anhydrous ZnSO₄, we will follow these steps:

### Step 1: Determine the mass of water absorbed
The initial mass of the anhydrous ZnSO₄ is given as 1.61 g, and the final mass after absorbing moisture is 2.87 g.

**Calculation:**
Mass of water absorbed = Final mass - Initial mass
= 2.87 g - 1.61 g
= 1.26 g

### Step 2: Calculate the moles of anhydrous ZnSO₄
First, we need to find the molar mass of ZnSO₄. The molar mass can be calculated as follows:
- Molar mass of Zn = 65 g/mol
- Molar mass of S = 32 g/mol
- Molar mass of O = 16 g/mol × 4 = 64 g/mol

Total molar mass of ZnSO₄ = 65 + 32 + 64 = 161 g/mol

Now, we can calculate the number of moles of anhydrous ZnSO₄:
**Calculation:**
Moles of ZnSO₄ = Mass / Molar mass
= 1.61 g / 161 g/mol
= 0.01 mol

### Step 3: Calculate the moles of water absorbed
Next, we calculate the moles of water (H₂O) absorbed. The molar mass of water is:
- Molar mass of H₂O = 2 × 1 + 16 = 18 g/mol

**Calculation:**
Moles of water = Mass / Molar mass
= 1.26 g / 18 g/mol
= 0.07 mol

### Step 4: Determine the value of x in ZnSO₄·xH₂O
From the previous calculations, we have:
- Moles of ZnSO₄ = 0.01 mol
- Moles of H₂O = 0.07 mol

The ratio of moles of water to moles of ZnSO₄ will give us the value of x:
**Calculation:**
x = Moles of H₂O / Moles of ZnSO₄
= 0.07 mol / 0.01 mol
= 7

### Step 5: Write the molecular formula of the hydrated salt
Now that we have determined the value of x, we can write the molecular formula of the hydrated salt:
ZnSO₄·7H₂O

### Final Answer:
The molecular formula of the hydrated salt is **ZnSO₄·7H₂O**.

---