The velocity of an oxygen molecule at the same temperature can be calculated using the equation v(o2) = √(3R/32) * v(co2), where v(co2) is the velocity of the carbon dioxide molecule. Plugging in the values, we find that the velocity of the oxygen molecule is approximately 38.4 m/s.
At a given temperature, the velocities of gas molecules are related to their molar masses. This relationship is given by the equation:
v = √(3RT/M)
where v is the velocity of the molecule, R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the molecule.
In this case, we are given the velocity of a carbon dioxide molecule, v(co2) = 45.0 m/s. We are asked to find the velocity of an oxygen molecule at the same temperature.
To find the velocity of the oxygen molecule, we need to compare the molar masses of carbon dioxide and oxygen. The molar mass of carbon dioxide (CO2) is approximately 44 g/mol, while the molar mass of oxygen (O2) is approximately 32 g/mol.
Using the given velocity of the carbon dioxide molecule, we can rearrange the equation to solve for the velocity of the oxygen molecule:
v(o2) = √(3RT/M(o2))
where M(o2) is the molar mass of oxygen.
Substituting the values into the equation, we have:
v(o2) = √(3RT/32)
Since the temperature is the same for both molecules, the value of T remains constant. Therefore, we can ignore it for the purpose of comparison.
To find the velocity of the oxygen molecule, we need to calculate the square root of (3R/32) times the velocity of the carbon dioxide molecule:
v(o2) = √(3R/32) * v(co2)
Plugging in the value of the velocity of carbon dioxide (45.0 m/s) and simplifying the equation, we find:
v(o2) = √(3/32) * 45.0 m/s
Calculating this expression, we find that the velocity of an oxygen molecule at the same temperature is approximately 38.4 m/s.
So, at the same temperature, the velocity of an oxygen molecule is approximately 38.4 m/s, based on the molar mass ratio and the given velocity of a carbon dioxide molecule.