Total number of sulphate ions present in 3.92 g of chromic sulphate is (Cr=52, S=32, O=16)

Options

A. `1.8xx10^(22)`
B. `1.8xx10^(23)`
C. `1.2xx10^(21)`
D. `6xx10^(23)`

Answer

To find the total number of sulfate ions present in 3.92 g of chromic sulfate, we will follow these steps:

### Step 1: Determine the formula of chromic sulfate.
The formula for chromic sulfate is \( \text{Cr}_2(\text{SO}_4)_3 \).

### Step 2: Calculate the molar mass of chromic sulfate.
To calculate the molar mass, we need to sum the atomic masses of all the atoms in the formula:
- Chromium (Cr): 2 atoms × 52 g/mol = 104 g/mol
- Sulfur (S): 3 atoms × 32 g/mol = 96 g/mol
- Oxygen (O): 12 atoms (4 from each sulfate ion, and there are 3 sulfate ions) × 16 g/mol = 192 g/mol

Now, add these together:
\[ \text{Molar mass} = 104 + 96 + 192 = 392 \text{ g/mol} \]

### Step 3: Calculate the number of moles of chromic sulfate in 3.92 g.
Using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{3.92 \text{ g}}{392 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 4: Calculate the number of molecules of chromic sulfate.
Using Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} = 0.01 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 6.022 \times 10^{21} \text{ molecules} \]

### Step 5: Calculate the total number of sulfate ions.
Since each molecule of chromic sulfate contains 3 sulfate ions:
\[ \text{Total sulfate ions} = \text{Number of molecules} \times 3 = 6.022 \times 10^{21} \text{ molecules} \times 3 = 1.8066 \times 10^{22} \text{ sulfate ions} \]
Rounding this gives:
\[ \text{Total sulfate ions} \approx 1.8 \times 10^{22} \]

### Final Answer:
The total number of sulfate ions present in 3.92 g of chromic sulfate is approximately \( 1.8 \times 10^{22} \).

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