Understanding Kinetic Energy and Temperature
* Kinetic Energy: The energy of motion. The faster the molecules move, the higher their kinetic energy.
* Temperature: A measure of the average kinetic energy of the particles in a substance.
Key Formula:
The average kinetic energy of an ideal gas is directly proportional to its absolute temperature (in Kelvin):
```
KE = (3/2) * k * T
```
Where:
* KE = Average kinetic energy
* k = Boltzmann constant (1.38 × 10^-23 J/K)
* T = Absolute temperature (in Kelvin)
Calculations
1. Convert Temperatures to Kelvin:
* 0°C = 273.15 K
* 298 K (already in Kelvin)
2. Calculate Average Kinetic Energy at Each Temperature:
* KE (273.15 K) = (3/2) * (1.38 × 10^-23 J/K) * (273.15 K) ≈ 5.65 × 10^-21 J
* KE (298 K) = (3/2) * (1.38 × 10^-23 J/K) * (298 K) ≈ 6.17 × 10^-21 J
3. Find the Difference:
* KE (298 K) - KE (273.15 K) ≈ 6.17 × 10^-21 J - 5.65 × 10^-21 J ≈ 5.2 × 10^-22 J
Conclusion
The average kinetic energy of 1 mole of water at 298 K is approximately 5.2 × 10^-22 J higher than at 0°C (273.15 K).
