The weight of methane which occupies the same volume at STP as 7.5 gm of ethane is _________ g .

Answer

To find the weight of methane that occupies the same volume at STP as 7.5 grams of ethane, we can use the ideal gas law and the concept of molar mass. Here’s a step-by-step solution:

### Step 1: Understand the relationship between moles and weight
At STP (Standard Temperature and Pressure), equal volumes of gases contain equal numbers of moles. Therefore, we can set up a relationship between the weights of the two gases based on their molar masses.

### Step 2: Identify the molar masses
- The molar mass of methane (CH₄) is approximately 16 g/mol.
- The molar mass of ethane (C₂H₆) is approximately 30 g/mol.

### Step 3: Set up the equation
Let \( w \) be the weight of methane. Since the volume occupied by both gases is the same, we can write:
\[ \frac{w}{\text{Molar mass of methane}} = \frac{7.5 \text{ g}}{\text{Molar mass of ethane}} \]
Substituting the molar masses:
\[ \frac{w}{16} = \frac{7.5}{30} \]

### Step 4: Solve for \( w \)
Cross-multiply to solve for \( w \):
\[ w = 7.5 \times \frac{16}{30} \]

### Step 5: Calculate the value
Now, calculate \( w \):
\[ w = 7.5 \times \frac{16}{30} = 7.5 \times 0.5333 = 4 \text{ g} \]

### Final Answer
The weight of methane that occupies the same volume at STP as 7.5 grams of ethane is **4 grams**.

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