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 2.380 `gL^(−1)` at `25^o`C and 1 atm pressure. Hence the molar mass of the gas is:

Options

A. 56
B. 58
C. 60
D. 38

Explanation

To find the molar mass of the gas using the given density, we can use the ideal gas law and the relationship between density and molar mass. Here’s a step-by-step solution:

### Step 1: Write down 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 moles to mass and molar mass
The number of moles \( n \) can be expressed as:
\[ n = \frac{m}{M} \]
where:
- \( m \) = mass of the gas (in grams)
- \( M \) = molar mass of the gas (in g/mol)

### Step 3: Substitute \( n \) in the ideal gas law
Substituting \( n \) into the ideal gas law gives:
\[ PV = \frac{m}{M}RT \]

### Step 4: Rearrange the equation to find molar mass
Rearranging the equation to solve for molar mass \( M \):
\[ M = \frac{mRT}{PV} \]

### Step 5: Use density to relate mass and volume
Density \( d \) is defined as:
\[ d = \frac{m}{V} \]
Thus, we can express mass \( m \) as:
\[ m = dV \]

### Step 6: Substitute mass in the molar mass equation
Substituting \( m \) in the molar mass equation gives:
\[ M = \frac{dVRT}{PV} \]

### Step 7: Simplify the equation
The volume \( V \) cancels out:
\[ M = \frac{dRT}{P} \]

### Step 8: Substitute known values
Now, we can substitute the known values:
- Density \( d = 2.380 \, g/L \)
- Pressure \( P = 1 \, atm \)
- Gas constant \( R = 0.0821 \, L \cdot atm \cdot K^{-1} \cdot mol^{-1} \)
- Temperature \( T = 25^\circ C = 298 \, K \)

Substituting these values into the equation:
\[ M = \frac{(2.380 \, g/L)(0.0821 \, L \cdot atm \cdot K^{-1} \cdot mol^{-1})(298 \, K)}{1 \, atm} \]

### Step 9: Calculate the molar mass
Calculating the above expression:
\[ M = \frac{(2.380)(0.0821)(298)}{1} \]
\[ M = 58.00 \, g/mol \]

### Final Answer
The molar mass of the gas is **58 g/mol**.

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