Final answer:
The root-mean-square speed (RMS speed) of O2 molecules in a sample of oxygen gas at a temperature of 151°C can be calculated using the formula Urms = √((3 * k * T) / M), where k is the Boltzmann constant, T is the temperature in Kelvin, and M is the molar mass of O2.
Step-by-step explanation:
The root-mean-square speed (RMS speed) of O2 molecules in a sample of oxygen gas can be calculated using the formula:
Urms = √((3 * k * T) / M)
Where:
- Urms is the root-mean-square speed
- k is the Boltzmann constant (1.38 * 10^-23 J/K)
- T is the temperature in Kelvin
- M is the molar mass of O2 in kg/mol
Given that the temperature is 151°C, we need to convert it to Kelvin by adding 273.15. So, the temperature is 151 + 273.15 = 424.15 K.
Using the given molar mass of O2 (32.0 g/mol or 0.032 kg/mol), we can substitute these values into the formula to find the RMS speed.
Substituting: Urms = √((3 * 1.38 * 10^-23 J/K * 424.15 K) / 0.032 kg/mol)
Solving this equation will give us the RMS speed of O2 molecules in the given sample of oxygen gas at the temperature of 151°C.