The mole fraction of oxygen in a mixture of 7g of nitrogen and 8g of oxygen is:

Options

A. `(8)/(15)`
B. `0.5`
C. `0.25`
D. `1.0`

Answer

To find the mole fraction of oxygen in a mixture of nitrogen and oxygen, we can follow these steps:

### Step 1: Calculate the number of moles of nitrogen (N₂)
1. **Given mass of nitrogen (N₂)** = 7 g
2. **Molar mass of nitrogen (N₂)** = 14 g/mol (since nitrogen is diatomic, we take 14 g/mol for N₂)
3. **Number of moles of nitrogen (N₂)** = mass / molar mass = 7 g / 14 g/mol = 0.5 moles

### Step 2: Calculate the number of moles of oxygen (O₂)
1. **Given mass of oxygen (O₂)** = 8 g
2. **Molar mass of oxygen (O₂)** = 16 g/mol (since oxygen is diatomic, we take 16 g/mol for O₂)
3. **Number of moles of oxygen (O₂)** = mass / molar mass = 8 g / 16 g/mol = 0.5 moles

### Step 3: Calculate the total number of moles in the mixture
1. **Total number of moles** = moles of nitrogen + moles of oxygen
2. Total number of moles = 0.5 moles (N₂) + 0.5 moles (O₂) = 1.0 moles

### Step 4: Calculate the mole fraction of oxygen
1. **Mole fraction of oxygen (X_O₂)** = moles of oxygen / total moles
2. Mole fraction of oxygen = 0.5 moles (O₂) / 1.0 moles = 0.5

### Final Answer
The mole fraction of oxygen in the mixture is **0.5**.

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