7.00g of a gas occupies a volume of 4.1 litres at 300K and 1 atmosphere pressure. Calculate the molecular mass of the gas-

Options

A. `40 g mol^(-1)`
B. `42 g mol^(-1)`
C. ` 48 g mol^(-1)`
D. ` 45 g mol^(-1)`

Explanation

To calculate the molecular mass of the gas, we will use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = Pressure (in atm)
- \( V \) = Volume (in liters)
- \( n \) = Number of moles of gas
- \( R \) = Universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = Temperature (in Kelvin)

### Step 1: Identify the given values
- Mass of gas (m) = 7.00 g
- Volume (V) = 4.1 L
- Temperature (T) = 300 K
- Pressure (P) = 1 atm

### Step 2: Calculate the number of moles (n)
The number of moles \( n \) can be expressed in terms of mass and molecular mass (M):

\[ n = \frac{m}{M} \]

Where \( M \) is the molecular mass of the gas in g/mol.

### Step 3: Substitute \( n \) into the Ideal Gas Law
Substituting the expression for \( n \) into the Ideal Gas Law gives:

\[ PV = \left(\frac{m}{M}\right)RT \]

### Step 4: Rearrange the equation to solve for M
Rearranging the equation for \( M \):

\[ M = \frac{mRT}{PV} \]

### Step 5: Substitute the known values into the equation
Now, substituting the known values into the equation:

- \( m = 7.00 \, \text{g} \)
- \( R = 0.0821 \, \text{L·atm/(K·mol)} \)
- \( T = 300 \, \text{K} \)
- \( P = 1 \, \text{atm} \)
- \( V = 4.1 \, \text{L} \)

So,

\[ M = \frac{7.00 \times 0.0821 \times 300}{1 \times 4.1} \]

### Step 6: Calculate the molecular mass (M)
Calculating the numerator:

\[ 7.00 \times 0.0821 \times 300 = 1,726.2 \]

Now, divide by the volume:

\[ M = \frac{1,726.2}{4.1} \approx 42.0 \, \text{g/mol} \]

### Final Answer
The molecular mass of the gas is approximately **42 g/mol**.

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