* Temperature Dependence: The speed of gas molecules is directly related to their temperature. The hotter the gas, the faster the molecules move. To compare helium and argon, we need to know the temperature.
* Average Speed vs. Individual Speed: Gas molecules move at a range of speeds. We typically talk about the *average* speed of the molecules. Even at the same temperature, helium molecules will have a higher average speed than argon molecules.
* Root-Mean-Square Speed: A common way to measure the average speed of gas molecules is the "root-mean-square speed" (rms speed). It's calculated using the following formula:
```
v_rms = √(3RT/M)
```
where:
* v_rms is the root-mean-square speed
* R is the ideal gas constant
* T is the temperature in Kelvin
* M is the molar mass of the gas
How Helium is Faster:
* Lower Molar Mass: Helium has a much lower molar mass than argon (4 g/mol vs. 40 g/mol). This means that at the same temperature, helium molecules will move faster.
* Example: Let's say we have helium and argon at 298 K (25°C). Plugging these values into the formula above, we get:
* v_rms (He) = √(3 * 8.314 J/mol·K * 298 K / 0.004 kg/mol) ≈ 1352 m/s
* v_rms (Ar) = √(3 * 8.314 J/mol·K * 298 K / 0.04 kg/mol) ≈ 431 m/s
This shows that helium molecules move about 3 times faster than argon molecules at room temperature.
In conclusion: Helium moves faster than argon at the same temperature because it has a much lower molar mass.
