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 determine 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. The formula for rms speed of gas molecules is:
v = √(3kT / m)
Where:
v is the rms speed
k is the Boltzmann constant (1.38 x 10^-23 J/K)
T is the temperature in Kelvin
m is the molar mass of the gas in kilograms
Given that the molar mass of oxygen (O2) is 32 g/mol (or 0.032 kg/mol), we can convert it to kilograms by dividing by 1000:
m = 0.032 kg/mol
Now we can rearrange the formula and solve for the temperature T:
T = (v^2 * m) / (3k)
Substituting the given values:
T = (640^2 * 0.032) / (3 * 1.38 x 10^-23)
Calculating this using a calculator:
T = 178270 > 1.783 x 10^5 K
Therefore, the temperature at which the rms speed of oxygen molecules is 640 m/s is approximately 1.783 x 10^5 Kelvin.