Calculate the total K.E. of 1g of nitrogen at `300 K`. Molecule weight of nitrogen `= 28`.

Answer

To calculate the total kinetic energy (K.E.) of 1 gram of nitrogen gas at 300 K, we can use the formula for the kinetic energy of gas molecules. The total kinetic energy of a gas can be expressed as:

\[ \text{Total K.E.} = \frac{3}{2} nRT \]

where:
- \( n \) = number of moles of the gas,
- \( R \) = universal gas constant \( = 8.314 \, \text{J/(mol K)} \),
- \( T \) = temperature in Kelvin.

### Step 1: Calculate the number of moles of nitrogen
First, we need to find the number of moles of nitrogen in 1 gram. The molecular weight of nitrogen (N₂) is given as 28 g/mol.

\[ n = \frac{\text{mass}}{\text{molecular weight}} = \frac{1 \, \text{g}}{28 \, \text{g/mol}} = \frac{1}{28} \, \text{mol} \]

### Step 2: Substitute values into the K.E. formula
Now we can substitute the values of \( n \), \( R \), and \( T \) into the kinetic energy formula.

\[ \text{Total K.E.} = \frac{3}{2} \left(\frac{1}{28} \, \text{mol}\right) (8.314 \, \text{J/(mol K)}) (300 \, \text{K}) \]

### Step 3: Calculate the total kinetic energy
Now we calculate the total kinetic energy step by step.

1. Calculate \( nRT \):
\[ nRT = \left(\frac{1}{28}\right) (8.314) (300) = \frac{2494.2}{28} \approx 89.07 \, \text{J} \]

2. Now, calculate the total K.E.:
\[ \text{Total K.E.} = \frac{3}{2} \times 89.07 \approx 133.605 \, \text{J} \]

Thus, the total kinetic energy of 1 gram of nitrogen at 300 K is approximately **133.61 J**.