The molecular kinetic energy of 1 g of helium (molecular weight 4) at `127^(@)C` is (Given , R `=8.31 J"mol"^(-1)K^(-1)` )

Options

A. 12.84 J
B. 12.465 J
C. 14.34
D. 14.384 J

Explanation

To find the molecular kinetic energy of 1 g of helium at 127°C, we can follow these steps:

### Step 1: Convert the temperature from Celsius to Kelvin
The temperature in Celsius is given as 127°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
So,
\[ T = 127 + 273 = 400 \, K \]

### Step 2: Identify the molecular weight of helium
The molecular weight of helium is given as 4 g/mol.

### Step 3: Use the formula for average kinetic energy per mole
The average kinetic energy (KE) per mole of a monatomic gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the gas constant (8.31 J/mol·K) and \( T \) is the temperature in Kelvin.

### Step 4: Calculate the average kinetic energy per mole
Substituting the values into the formula:
\[ KE = \frac{3}{2} \times 8.31 \, \text{J/mol·K} \times 400 \, K \]
Calculating this gives:
\[ KE = \frac{3}{2} \times 8.31 \times 400 = 4986 \, J/mol \]

### Step 5: Calculate the average kinetic energy for 1 g of helium
Since we need the kinetic energy for 1 g of helium, we need to divide the kinetic energy per mole by the molecular weight:
\[ KE_{1g} = \frac{KE_{per mole}}{molecular \, weight} \]
\[ KE_{1g} = \frac{4986 \, J/mol}{4 \, g/mol} \]
Calculating this gives:
\[ KE_{1g} = 1246.5 \, J \]

### Final Answer
The molecular kinetic energy of 1 g of helium at 127°C is:
\[ KE_{1g} = 1246.5 \, J \]

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