In an attempt to prepare propane by Wurtz reaction 1 mole of methyl bromide and 1 mole of ethyl bromide are treated with sodium. Assuming equal probability for all possible reaction. How many g of propane will be obtained?

Options

A. 44 g
B. 22 g
C. 33 g
D. 14.67 g

Answer

To solve the problem of how many grams of propane will be obtained from the Wurtz reaction of 1 mole of methyl bromide and 1 mole of ethyl bromide treated with sodium, we can follow these steps:

### Step 1: Understand the Reaction
The Wurtz reaction involves the coupling of alkyl halides in the presence of sodium metal. Here, we have methyl bromide (CH₃Br) and ethyl bromide (C₂H₅Br).

### Step 2: Identify Possible Products
When methyl bromide and ethyl bromide react with sodium, the possible products are:
1. Propane (C₃H₈) from the reaction of CH₃Br and C₂H₅Br.
2. Butane (C₄H₁₀) from the coupling of two methyl bromide molecules (CH₃Br + CH₃Br).
3. Butane (C₄H₁₀) from the coupling of two ethyl bromide molecules (C₂H₅Br + C₂H₅Br).

### Step 3: Calculate the Probability of Each Product
Since we assume equal probability for all possible reactions, we can denote the probabilities of forming each product as follows:
- Probability of forming propane (C₃H₈) = 1/3
- Probability of forming butane from two methyl bromides (C₄H₁₀) = 1/3
- Probability of forming butane from two ethyl bromides (C₄H₁₀) = 1/3

### Step 4: Determine Moles of Propane Formed
Given that we have 1 mole of each alkyl halide, the moles of propane produced can be calculated as:
- Moles of propane = (1 mole of methyl bromide + 1 mole of ethyl bromide) × (1/3 probability) = 2 moles × (1/3) = 2/3 moles of propane.

### Step 5: Convert Moles of Propane to Grams
To find the mass of propane produced, we need to know the molar mass of propane (C₃H₈):
- Molar mass of C₃H₈ = (3 × 12.01 g/mol) + (8 × 1.008 g/mol) = 36.03 g + 8.064 g = 44.094 g/mol.

Now, we can calculate the mass of propane:
- Mass of propane = moles × molar mass = (2/3 moles) × (44.094 g/mol) = 29.396 g.

### Step 6: Final Answer
Thus, the total mass of propane obtained from the reaction is approximately **29.40 grams**.

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