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 ideal gas law and the equation for rms speed.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
The equation for rms speed is vrms = √((3RT) / M), where vrms is the rms speed, R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
In this case, we are dealing with oxygen molecules, which have a molar mass of 32 g/mol or 0.032 kg/mol.
To find the temperature at which the rms speed is 640 m/s, we need to rearrange the equation for vrms:
vrms = √((3RT) / M) => (vrms)^2 = (3RT) / M => T = (M * (vrms)^2) / (3R)
Plugging in the values, we have:
T = (0.032 kg/mol * (640 m/s)^2) / (3 * 8.314 J/(mol·K))
Calculating this expression, we find:
T ≈ 1202 K
Therefore, the temperature at which the root-mean-square speed of oxygen molecules is 640 m/s is approximately 1202 Kelvin.