The internal energy of 10 g of nitrogen at N. T. P. is about

Options

A. 2575 J
B. 2025 J
C. 3721 J
D. 4051 J

Answer

To find the internal energy of 10 g of nitrogen gas (N₂) at normal temperature and pressure (NTP), we can use the formula for internal energy \( U \) of an ideal gas:

\[ U = \frac{f}{2} n R T \]

Where:
- \( U \) is the internal energy,
- \( f \) is the degrees of freedom,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant (approximately \( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the temperature in Kelvin.

### Step 1: Determine the degrees of freedom \( f \)
For a diatomic gas like nitrogen (N₂), the degrees of freedom \( f \) is 5.

### Step 2: Calculate the number of moles \( n \)
To find the number of moles, we use the formula:

\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Given:
- Mass of nitrogen = 10 g
- Molar mass of nitrogen (N₂) = 28 g/mol (since each nitrogen atom has a mass of approximately 14 g)

Calculating the number of moles:

\[ n = \frac{10 \, \text{g}}{28 \, \text{g/mol}} \approx 0.357 \, \text{mol} \]

### Step 3: Use the temperature \( T \)
At normal temperature and pressure (NTP), the temperature \( T \) is 273 K.

### Step 4: Substitute the values into the internal energy formula
Now we can substitute the values into the internal energy formula:

\[ U = \frac{5}{2} \cdot n \cdot R \cdot T \]

Substituting \( n \approx 0.357 \, \text{mol} \), \( R = 8.314 \, \text{J/mol·K} \), and \( T = 273 \, \text{K} \):

\[ U = \frac{5}{2} \cdot 0.357 \cdot 8.314 \cdot 273 \]

### Step 5: Calculate the internal energy
Now, we can calculate:

\[ U = \frac{5}{2} \cdot 0.357 \cdot 8.314 \cdot 273 \approx 2026.53 \, \text{J} \]

Rounding this value gives us approximately:

\[ U \approx 2025 \, \text{J} \]

### Final Answer
The internal energy of 10 g of nitrogen at NTP is approximately **2025 Joules**.

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