At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilom has a mass of 32kg.
To find the temperature at which the root-mean-square (RMS) speed of oxygen molecules is 640 m/s, we can use the formula for RMS speed:
RMS speed = √(3kT/m)
Where:
- RMS speed is the root-mean-square speed of the molecules
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the mass of one molecule in kg
Given that 1 kilom (molar mass) of oxygen has a mass of 32 kg, this means that the molar mass (M) of oxygen is 32 g/mol (grams per mole).
To calculate the mass of one oxygen molecule, we divide the molar mass by Avogadro's number (6.022 x 10^23 mol^-1):
Molecular mass = M / Avogadro's number
m = (32 g/mol) / (6.022 x 10^23 mol^-1)
Now, we have the value of m, which is the mass of one oxygen molecule.
To find the temperature (T) at which the RMS speed is 640 m/s, we rearrange the formula:
T = (RMS speed)^2 * m / (3k)
Substituting the given values:
T = (640 m/s)^2 * (mass of one molecule) / (3 * Boltzmann constant)
Now, let's calculate the temperature using these values:
T = (640 m/s)^2 * (32 kg / 6.022 x 10^23) / (3 * 1.38 x 10^-23 J/K)
T ≈ 247704 K
Therefore, at approximately 247704 Kelvin, the root-mean-square speed of oxygen molecules will be 640 m/s.