Calculate the root mean square velocity of the oxygen gas (O2) molecules at 77 °C. (R =8.314 Kg.m²/S².mol.K). (atomic mass of O-15.999 g/mol)
16.52 x 105 m/s
2.72 x 105 m/s
272.82 x 10 m/s
5.22 x102 m/s
16.52 X 10 to the power of 5 m/s
2.72 X 10 to the power of 5 m/s
5.22 x10 squared m/s
272.82 X 10 m/s
(Note: I'm assuming you meant 77 °C and not 77 K, as the latter would result in a negative temperature)
The root mean square velocity, u rms, of a gas is given by the equation:
u 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 = (77 + 273.15) K = 350.15 K
Next, we can plug in the values:
u rms = √(3 x 8.314 x 350.15 / 0.032)
where we converted O2's molar mass from grams to kilograms (0.032 kg/mol).
Simplifying this gives:
u rms = 466.4 m/s
Rounding to two significant figures gives:
u rms = 4.7 x 10^2 m/s
Therefore, the closest answer choice is 5.22 x 10^2 m/s.
To calculate the root mean square velocity of oxygen gas molecules at 77 °C, we can use the following formula:
Vrms = √((3 * R * T) / M)
Where:
Vrms = root mean square velocity
R = ideal gas constant (8.314 Kg.m²/S².mol.K)
T = temperature in Kelvin (convert 77 °C to Kelvin by adding 273.15: 77 + 273.15 = 350.15 K)
M = molar mass of oxygen gas (O2), which is 2 * atomic mass of oxygen (O) = 2 * 15.999 g/mol = 31.998 g/mol
Plugging in the values into the formula, we have:
Vrms = √((3 * 8.314 * 350.15) / 31.998)
Calculating this, we get:
Vrms ≈ 487.57 m/s
Therefore, the correct option is not among the provided answer choices.