1. Understand Internal Energy
Internal energy (U) is the total energy contained within a system. For an ideal gas, internal energy is primarily due to the kinetic energy of the molecules.
2. The Formula
For an ideal gas, the internal energy is given by:
U = (3/2) * n * R * T
Where:
* U = Internal energy
* n = Number of moles (4.50 mol)
* R = Ideal gas constant (8.314 J/mol·K)
* T = Temperature in Kelvin (25°C + 273.15 = 298.15 K)
3. Calculation
U = (3/2) * 4.50 mol * 8.314 J/mol·K * 298.15 K
U ≈ 16773 J
Therefore, the internal energy of 4.50 mol of N₂ gas at 25°C is approximately 16773 J.
Important Note: This calculation assumes the N₂ gas behaves ideally. In reality, real gases deviate from ideal behavior at high pressures and low temperatures.
