The density of a gas at S.T.P is 1.50 grams per litre. The molecular weight of the gas is

Options

A. 28
B. 30
C. 33.6
D. 35

Explanation

To find the molecular weight of the gas given its density at STP, we can follow these steps:

### Step 1: Understand the relationship between density, molecular weight, and molar volume.
The formula relating these quantities is:
\[ \text{Density} = \frac{\text{Molecular Weight}}{\text{Molar Volume}} \]
Where:
- Density (d) is given in grams per liter (g/L).
- Molecular Weight (M) is what we need to find (in grams per mole, g/mol).
- Molar Volume (V) at STP is known to be 22.4 L for 1 mole of gas.

### Step 2: Substitute the known values into the formula.
We know:
- Density \( d = 1.50 \, \text{g/L} \)
- Molar Volume \( V = 22.4 \, \text{L} \)

Using the formula:
\[ 1.50 = \frac{M}{22.4} \]

### Step 3: Rearrange the equation to solve for Molecular Weight (M).
To find M, we can rearrange the equation:
\[ M = d \times V \]

### Step 4: Substitute the values into the rearranged equation.
Now, substituting the known values:
\[ M = 1.50 \, \text{g/L} \times 22.4 \, \text{L} \]

### Step 5: Calculate the Molecular Weight.
Now we perform the multiplication:
\[ M = 1.50 \times 22.4 = 33.6 \, \text{g/mol} \]

### Conclusion:
The molecular weight of the gas is \( 33.6 \, \text{g/mol} \).

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