Calculate the number of moles of hydrogen contained in `18` liters of a gas at `27^(@)C` and `0.92` bar pressure. If the mass of hydrogen is found to be `1.350g`. Calculate the molecular mass of hydrogen.

Explanation

To solve the problem step by step, we will use the ideal gas equation and the relationship between mass, moles, and molecular mass.

### Step 1: Convert Temperature to Kelvin
The temperature is given as \(27^\circ C\). To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
\[ T = 27 + 273 = 300 \, K \]

### Step 2: Use the Ideal Gas Equation
The ideal gas equation is given by:
\[ PV = nRT \]
Where:
- \(P\) = pressure in bar = 0.92 bar
- \(V\) = volume in liters = 18 L
- \(R\) = ideal gas constant = 0.083 L·bar/(K·mol)
- \(T\) = temperature in Kelvin = 300 K

We need to rearrange the equation to solve for the number of moles \(n\):
\[ n = \frac{PV}{RT} \]

### Step 3: Substitute the Values
Now, substitute the values into the equation:
\[ n = \frac{(0.92 \, \text{bar}) \times (18 \, \text{L})}{(0.083 \, \text{L·bar/(K·mol)}) \times (300 \, K)} \]

### Step 4: Calculate the Number of Moles
Calculating the numerator:
\[ 0.92 \times 18 = 16.56 \, \text{bar·L} \]
Calculating the denominator:
\[ 0.083 \times 300 = 24.9 \, \text{L·bar/(K·mol)} \]
Now, substituting these into the equation:
\[ n = \frac{16.56}{24.9} \approx 0.6667 \, \text{mol} \]

### Step 5: Calculate the Molecular Mass of Hydrogen
We know the mass of hydrogen is given as \(1.350 \, g\). The molecular mass \(M\) can be calculated using the formula:
\[ M = \frac{\text{mass}}{n} \]
Substituting the values:
\[ M = \frac{1.350 \, g}{0.6667 \, mol} \approx 2.025 \, g/mol \]

### Final Answer
The molecular mass of hydrogen is approximately \(2.025 \, g/mol\).

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