Calculate the average speed of an oxygen molecule (with a mass of 5.3e-26 kg) at room temperature (300 Kelvin)show your work

To calculate the average speed of an oxygen molecule at room temperature, we can use the root mean square (RMS) speed formula. The RMS speed is a measure of the average speed of gas particles in a sample.

The formula to calculate the RMS speed is:
v = √(3kT / m)

Where:
v is the RMS speed
k is the Boltzmann constant (1.38 × 10^-23 J/K)
T is the temperature in Kelvin
m is the mass of the molecule

Now, let's substitute the given values into the formula:

m = 5.3 × 10^-26 kg
T = 300 K
k = 1.38 × 10^-23 J/K

v = √(3 * (1.38 × 10^-23J/K) * (300 K) / (5.3 × 10^-26 kg))

Simplifying the equation:
v = √(4.14 × 10^-21 J / 5.3 × 10^-26 kg)

Now, divide the numbers inside the square root:
v = √(7.80 × 10^4 m^2/s^2)

Finally, take the square root to find the average speed:
v ≈ 279 m/s

Therefore, the average speed of an oxygen molecule at room temperature is approximately 279 m/s.