The density of a gas is 2.5g/L at `127^@C` and 1 atm. The molecular weight of the gas is 

Options

A. 82.1
B. 41.05
C. 56
D. 28

Explanation

To find the molecular weight of the gas using the given density, temperature, and pressure, we can use the formula derived from the ideal gas law. Here’s a step-by-step solution:

### Step 1: Convert the temperature from Celsius to Kelvin
The temperature in Celsius is given as 127°C. To convert it to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
Substituting the given value:
\[ T(K) = 127 + 273.15 = 400.15 \, K \]

### Step 2: Use the formula for molecular weight
The molecular weight (MW) can be calculated using the formula:
\[ MW = \frac{\rho \cdot R \cdot T}{P} \]
Where:
- \(\rho\) = density of the gas = 2.5 g/L
- \(R\) = universal gas constant = 0.0821 L·atm/(mol·K)
- \(T\) = temperature in Kelvin = 400.15 K
- \(P\) = pressure = 1 atm

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ MW = \frac{2.5 \, g/L \cdot 0.0821 \, L \cdot atm/(mol \cdot K) \cdot 400.15 \, K}{1 \, atm} \]

### Step 4: Calculate the molecular weight
Calculating the numerator:
\[ 2.5 \cdot 0.0821 \cdot 400.15 = 82.1 \, g/mol \]
Now, since the pressure is 1 atm, we can simplify:
\[ MW = \frac{82.1}{1} = 82.1 \, g/mol \]

### Final Answer
The molecular weight of the gas is **82.1 g/mol**.

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