A gas cylinder was found unattended in a public place. The investigating team took the collected samples from it. The density of the gas was found to be 1.380 `gL^(−1)` at `35^o`C and 1 atm pressure. Hence the molar mass of the gas is:

Options

A. 25.47g/mol
B. 42g/mol
C. 34.89g/mol
D. 40g/mol

Explanation

To find the molar mass of the gas, we can use the Ideal Gas Law and the relationship between density and molar mass. Here’s the step-by-step solution:

### Step 1: Understand the Ideal Gas Law
The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature (in Kelvin)

### Step 2: Relate Density to Molar Mass
We know that:
\[ n = \frac{mass}{molar \, mass} \]
Thus, we can rewrite the Ideal Gas Law in terms of density (\( d \)):
\[ d = \frac{mass}{volume} \]
Substituting \( n \) into the Ideal Gas Law gives:
\[ PV = \frac{mass}{molar \, mass} \cdot RT \]
Rearranging this, we can express molar mass as:
\[ molar \, mass = \frac{density \cdot R \cdot T}{P} \]

### Step 3: Convert Temperature to Kelvin
The temperature is given as \( 35^\circ C \). To convert this to Kelvin:
\[ T(K) = 35 + 273.15 = 308.15 \, K \]

### Step 4: Substitute Values into the Molar Mass Equation
Now we can substitute the known values into the equation:
- Density (\( d \)) = 1.380 g/L
- Pressure (\( P \)) = 1 atm
- Gas constant (\( R \)) = 0.0821 L·atm/(K·mol)
- Temperature (\( T \)) = 308.15 K

The formula becomes:
\[ molar \, mass = \frac{1.380 \, g/L \cdot 0.0821 \, L \cdot atm/(K \cdot mol) \cdot 308.15 \, K}{1 \, atm} \]

### Step 5: Calculate Molar Mass
Now, performing the calculation:
\[ molar \, mass = \frac{1.380 \cdot 0.0821 \cdot 308.15}{1} \]
\[ molar \, mass = 34.89 \, g/mol \]

### Conclusion
The molar mass of the gas is approximately \( 34.89 \, g/mol \).