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).
5.22 x10 squared m/s
272.82 x 10 m/s
2.72 x 10 to the power of 5m/s
16.52 x 10 to the power of 5 m/s
The correct answer is 516.9 m/s.
To calculate the root mean square velocity of oxygen gas molecules at 77 °C, we can use the following equation:
u = √(3RT/M)
where u 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 = 350 K), and M is the molar mass of oxygen (15.999 g/mol).
First, let's convert the molar mass of oxygen to kg/mol:
M = 15.999 g/mol / 1000 g/kg = 0.015999 kg/mol
Now we can substitute the values into the equation:
u = √(3 x 8.314 Kg.m²/S².mol.K x 350 K / 0.015999 kg/mol)
u = 516.9 m/s
Therefore, the root mean square velocity of oxygen gas molecules at 77 °C is approximately 516.9 m/s.
To calculate the root mean square velocity of oxygen gas molecules at 77 °C, we can use the following formula:
v = sqrt((3 * R * T) / M)
Where:
v is the root mean square velocity
R is the ideal gas constant (8.314 Kg.m²/S².mol.K)
T is the temperature in Kelvin (convert 77 °C to Kelvin: 77 + 273 = 350 K)
M is the molar mass of oxygen (15.999 g/mol)
Plugging in the values into the formula:
v = sqrt((3 * 8.314 * 350) / 15.999)
v = sqrt(6937.14 / 15.999)
v = sqrt(433.61)
v ≈ 20.8 m/s
Therefore, the correct answer is not one of the options provided. The root mean square velocity of oxygen gas molecules at 77 °C is approximately 20.8 m/s.