The Kinetic Molecular Theory establishes a direct, proportional relationship between the absolute temperature of a substance and the average kinetic energy of its particles. As thermal energy is transferred into a system, the average kinetic energy increases, resulting in greater translational, vibrational, or rotational velocities.
Temperature & Average Kinetic Energy
The temperature, T, in Kelvin (K) is a measure of the average kinetic energy \(E_k\) of particles.
The Kelvin Scale
The Kelvin scale is the absolute temperature scale used in all thermodynamic work. Unlike Celsius, it has no negative values. It starts from absolute zero (0 K), the theoretical point at which all particle motion ceases.
Kelvin vs Celsius Scale
T (K) = T (°C) + 273.15
Note: one Kelvin has the exact same incremental value as one degree Celsius. An increase of 10°C = an increase of 10 K.
Note: one Kelvin has the exact same incremental value as one degree Celsius. An increase of 10°C = an increase of 10 K.
Heat vs Temperature
A frequent source of confusion. And a common exam trap. Is the failure to distinguish between heat and temperature.
Heat (q)
- A form of energy transfer between objects at different temperatures
- Measured in Joules (J) or kilojoules (kJ)
- A bathtub of lukewarm water contains more heat energy than a cup of boiling water
Temperature (T)
- A measure of the average kinetic energy of the particles
- Measured in Kelvin (K) or degrees Celsius (°C)
- The boiling water has a higher temperature because its particles move faster on average
Always Use Kelvin in Gas & Thermodynamic Equations
In thermodynamic definitions (e.g. Standard enthalpy changes), conditions must be expressed using the Kelvin scale. The ideal gas equation \(pV = nRT\) requires temperature in Kelvin. Using Celsius will give a completely wrong answer. Always convert to Kelvin before substituting into any equation.
Kinetic Energy and Molecular Mass
A common misconception is that heavier gas particles have more kinetic energy than lighter ones at the same temperature. This is incorrect.
Equal Temperature Means Equal Average Kinetic Energy
At a given temperature, all gases possess the same average kinetic energy, regardless of their molecular mass. Since \(E_k = \frac{1}{2}mv^2\), heavier particles (larger \(m\)) must move at a slower velocity (\(v\)) to maintain the same \(E_k\).
Significant Figures in Temperature Conversions
Pay attention to significant figures when converting temperatures. For example, \(25.0°C + 273.15 = 298.15\), which rounds to 298.2 K (one decimal place to match the input). The IB expects precision in your conversions.
Temperature Scale Conversions
Convert 25 °C to Kelvin:
T(K) = T(°C) + 273 = 25 + 273 = 298 K
Convert 373 K to Celsius:
T(°C) = T(K) - 273 = 373 - 273 = 100 °C
Why 298 K matters: Standard conditions in chemistry are defined at 298 K (25 °C). You will see this temperature frequently in thermodynamics and equilibrium questions.
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