What is the emprical formula of vanadium oxide , if `2.74g` of the metal oxide contains `1.53g` of metal ?

Options

A. `V_(2)O_(3)`
B. VO
C. `V_(2)O_(5)`
D. `V_(2)O_(7)`

Answer

To find the empirical formula of vanadium oxide given that 2.74 g of the metal oxide contains 1.53 g of metal, we can follow these steps:

### Step 1: Calculate the mass of oxygen in the metal oxide.
The mass of the metal oxide is given as 2.74 g, and the mass of the metal (vanadium) is given as 1.53 g. Therefore, the mass of oxygen can be calculated as follows:

\[ \text{Mass of Oxygen} = \text{Mass of Metal Oxide} - \text{Mass of Metal} \]
\[ \text{Mass of Oxygen} = 2.74 \, \text{g} - 1.53 \, \text{g} = 1.21 \, \text{g} \]

### Step 2: Calculate the number of moles of vanadium and oxygen.
Next, we need to calculate the number of moles of vanadium and oxygen.

- The molar mass of vanadium (V) is approximately 51 g/mol.
- The molar mass of oxygen (O) is approximately 16 g/mol.

**Moles of Vanadium:**
\[ \text{Moles of V} = \frac{\text{Mass of V}}{\text{Molar Mass of V}} = \frac{1.53 \, \text{g}}{51 \, \text{g/mol}} \approx 0.03 \, \text{mol} \]

**Moles of Oxygen:**
\[ \text{Moles of O} = \frac{\text{Mass of O}}{\text{Molar Mass of O}} = \frac{1.21 \, \text{g}}{16 \, \text{g/mol}} \approx 0.0756 \, \text{mol} \]

### Step 3: Determine the simplest mole ratio.
Now, we need to find the simplest ratio of moles of vanadium to moles of oxygen.

To do this, we divide the number of moles of each element by the smallest number of moles calculated:

**For Vanadium:**
\[ \text{Ratio of V} = \frac{0.03}{0.03} = 1 \]

**For Oxygen:**
\[ \text{Ratio of O} = \frac{0.0756}{0.03} \approx 2.52 \approx 2.5 \]

### Step 4: Convert the ratio to whole numbers.
Since we have a ratio of 1 for vanadium and approximately 2.5 for oxygen, we can multiply both ratios by 2 to convert them to whole numbers:

\[ \text{Vanadium: } 1 \times 2 = 2 \]
\[ \text{Oxygen: } 2.5 \times 2 = 5 \]

### Step 5: Write the empirical formula.
The empirical formula based on the whole number ratios is:

\[ \text{Empirical Formula} = V_2O_5 \]

### Final Answer:
The empirical formula of vanadium oxide is **V₂O₅**.

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