* Average speed of gas molecules: This is related to the temperature of the gas. The higher the temperature, the faster the molecules move on average. This is described by the root-mean-square (RMS) speed, which is calculated using the following equation:
```
v_rms = sqrt(3kT/m)
```
where:
* v_rms is the RMS speed
* k is Boltzmann's constant (1.38 × 10^-23 J/K)
* T is the temperature in Kelvin (Celsius + 273.15)
* m is the mass of one molecule (in kg)
* Velocity: This refers to the speed and direction of an object.
* 1050 mph: This is a velocity, not a speed. It tells us how fast something is moving *and* in what direction.
Here's why the question is a bit tricky:
* You can't directly convert 1050 mph to the average speed of nitrogen molecules. The molecules in air are moving randomly in all directions, so their average speed doesn't correspond to a single velocity.
* The average speed of nitrogen molecules at 20°C is determined by the temperature, not by the velocity of a particular object.
To calculate the average speed of N2 molecules at 20°C:
1. Convert Celsius to Kelvin: 20°C + 273.15 = 293.15 K
2. Find the mass of an N2 molecule: The molecular weight of N2 is 28 g/mol. To convert this to kg/molecule, divide by Avogadro's number (6.022 x 10^23 molecules/mol) and by 1000 g/kg:
(28 g/mol) / (6.022 x 10^23 molecules/mol) / (1000 g/kg) = 4.65 x 10^-26 kg/molecule
3. Plug values into the RMS speed equation:
```
v_rms = sqrt(3 * 1.38 × 10^-23 J/K * 293.15 K / 4.65 x 10^-26 kg)
v_rms ≈ 515 m/s
```
Therefore, the average speed of N2 molecules in air at 20°C is approximately 515 meters per second.
