Calculate the root mean square velocity of theoxygen gas (O2) molecules at 77 °C. (R =8.314 Kg.m²/S².mol.K). (atomic mass of O-15.999 g/mol).
We can use the root mean square velocity formula:
v rms = √(3RT/M)
where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
First, we need to convert the temperature to Kelvin:
77 °C = 350 K
Next, we convert the molar mass of oxygen from g/mol to kg/mol:
M = 15.999 g/mol = 0.015999 kg/mol
Now, we can plug in the values and solve:
v rms = √(3 * 8.314 Kg.m²/S².mol.K * 350 K / 0.015999 kg/mol)
v rms = √(622.38 m²/s²)
v rms = 24.95 m/s
Therefore, the root mean square velocity of the oxygen gas molecules at 77 °C is 24.95 m/s.
To calculate the root mean square velocity of oxygen gas (O2) molecules at 77 °C, you can use the formula:
v = sqrt((3 * R * T) / M)
Where:
v is the root mean square velocity
R is the gas constant (8.314 Kg.m²/S².mol.K)
T is the temperature in Kelvin (77 °C = 77 + 273 = 350 K)
M is the molar mass of O2 (2 * atomic mass of O)
Note: The atomic mass of O is given as 15.999 g/mol, so the molar mass of O2 is 2 * 15.999 = 31.998 g/mol.
Now, we can substitute the values into the formula and calculate the root mean square velocity:
v = sqrt((3 * 8.314 * 350) / 31.998)
v = sqrt(23.166 / 31.998)
v = sqrt(0.7236)
v ≈ 0.850 m/s
Therefore, the root mean square velocity of oxygen gas (O2) molecules at 77 °C is approximately 0.850 m/s.