KEY2CHEM

Temperature

Temperature is a measure of the average kinetic energy of atoms and molecules. The Kelvin scale is the absolute temperature scale, with a minimum temperature of $$0 \text{ K}$$ (absolute zero). As the temperature nears absolute zero, the average kinetic energy of the particles in the sample nears zero.

Example 1.

Which gas sample is expected to have the greatest average kinetic energy?

A. $$\require{mhchem}\ce{He}\; \text{at} \;298\text{ K}$$

B. $$\require{mhchem}\ce{H2}\; \text{at} \;100\text{ K}$$

C. $$\require{mhchem}\ce{Ar}\; \text{at} \;500\text{ K}$$

Solution

C. $$\require{mhchem}\ce{Ar}\; \text{at} \;500\text{ K}$$

Temperature is a measure of average kinetic energy of atoms and molecules. Increasing the temperature (regardless of identity of gas) increases average kinetic energy. All gases at the same temperature have the same average kinetic energy; however, gases with different masses will have different average molecular speeds.

Example 2.

Which gas sample is expected to have the fastest average molecular speed at $$298\text{ K}$$?

A. $$\require{mhchem}\ce{Ar}$$

B. $$\require{mhchem}\ce{Ne}$$

C. $$\require{mhchem}\ce{He}$$

Solution

C. $$\require{mhchem}\ce{He}$$

At the same temperature, all gases have the same average molecular speed. Since $$E_k = \frac{1}{2} mv^2$$, gases with lower molar masses ($$m$$) will move with higher velocities ($$v$$), or speed.

Example 3.

Based on the graph below of the same gas at three temperatures, which temperature is the highest?

A. $$T_1$$

B. $$T_2$$

C. $$T_3$$

Solution

C. $$T_3$$

At the highest temperature, particles have the greatest average kinetic energy and will be distributed with the widest distribution of molecular speeds (with a higher average molecular speed).