A gaseous mixture is composed of equal number of moles of `CH_4, C_2H_6 and C_2H_2`. Determine the average molecular mass of mixture (in amu)

Answer

To determine the average molecular mass of a gaseous mixture composed of equal numbers of moles of `CH4`, `C2H6`, and `C2H2`, we can follow these steps:

### Step 1: Identify the Molar Masses
First, we need to find the molar masses of each component in the mixture:
- For `CH4` (Methane):
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Total = 12 + 4 = **16 g/mol**

- For `C2H6` (Ethane):
- Carbon (C) = 12 g/mol × 2 = 24 g/mol
- Hydrogen (H) = 1 g/mol × 6 = 6 g/mol
- Total = 24 + 6 = **30 g/mol**

- For `C2H2` (Acetylene):
- Carbon (C) = 12 g/mol × 2 = 24 g/mol
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol
- Total = 24 + 2 = **26 g/mol**

### Step 2: Define the Number of Moles
Let the number of moles of each gas be `x`. Since there are equal numbers of moles of each gas, we have:
- Moles of `CH4` = `x`
- Moles of `C2H6` = `x`
- Moles of `C2H2` = `x`

### Step 3: Calculate the Total Mass of the Mixture
Now, we calculate the total mass contributed by each gas:
- Mass of `CH4` = Moles × Molar Mass = `x × 16 = 16x`
- Mass of `C2H6` = Moles × Molar Mass = `x × 30 = 30x`
- Mass of `C2H2` = Moles × Molar Mass = `x × 26 = 26x`

Now, we sum these masses to get the total mass of the mixture:
- Total Mass = Mass of `CH4` + Mass of `C2H6` + Mass of `C2H2`
- Total Mass = `16x + 30x + 26x = 72x`

### Step 4: Calculate the Total Number of Moles
The total number of moles in the mixture is:
- Total Moles = Moles of `CH4` + Moles of `C2H6` + Moles of `C2H2`
- Total Moles = `x + x + x = 3x`

### Step 5: Calculate the Average Molecular Mass
The average molecular mass of the mixture can be calculated using the formula:
\[ \text{Average Molecular Mass} = \frac{\text{Total Mass}}{\text{Total Moles}} = \frac{72x}{3x} \]
Here, the `x` cancels out:
\[ \text{Average Molecular Mass} = \frac{72}{3} = 24 \text{ g/mol} \]

### Conclusion
The average molecular mass of the mixture is **24 g/mol**, which is equivalent to **24 amu** (since 1 g/mol is approximately equal to 1 amu).

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