182 g of `V_(2)O_(5)` contains :

Options

A. 5 mole of oxygen atom
B. 2 mole of V atom
C. 1 mole of oxygen atom
D. 2.5 mole of oxygen atom

Answer

To solve the question regarding how many moles of vanadium (V) and oxygen (O) are contained in 182 g of \( V_2O_5 \), we will follow these steps:

### Step 1: Calculate the Molar Mass of \( V_2O_5 \)

The molar mass of \( V_2O_5 \) can be calculated by adding the molar masses of its constituent elements:

- Molar mass of Vanadium (V) = 51 g/mol
- Molar mass of Oxygen (O) = 16 g/mol

The formula for \( V_2O_5 \) contains:
- 2 Vanadium atoms
- 5 Oxygen atoms

Now, calculate the total molar mass:

\[ \text{Molar mass of } V_2O_5 = (2 \times 51) + (5 \times 16) = 102 + 80 = 182 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( V_2O_5 \)

Using the formula for moles:

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

Substituting the values:

\[ \text{Number of moles of } V_2O_5 = \frac{182 \text{ g}}{182 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Determine the Number of Moles of Vanadium (V)

From the chemical formula \( V_2O_5 \), we see that there are 2 moles of Vanadium for every mole of \( V_2O_5 \):

\[ \text{Number of moles of V} = 2 \times \text{Number of moles of } V_2O_5 = 2 \times 1 = 2 \text{ moles} \]

### Step 4: Determine the Number of Moles of Oxygen (O)

Similarly, from the formula \( V_2O_5 \), there are 5 moles of Oxygen for every mole of \( V_2O_5 \):

\[ \text{Number of moles of O} = 5 \times \text{Number of moles of } V_2O_5 = 5 \times 1 = 5 \text{ moles} \]

### Final Summary

- Number of moles of Vanadium (V) = 2 moles
- Number of moles of Oxygen (O) = 5 moles