Calculate the root mean speed of oxygen gas O2 at 27.0 oC. (R=8.314 Kg.m3/s2.K.mol)
(Molar mass: O= 16 g/mol)
First, we need to convert the temperature from Celsius to Kelvin:
27.0°C + 273.15 = 300.15 K
Next, we can use the formula for root mean speed:
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.
Plugging in the values:
u rms = √(3 * 8.314 * 300.15/0.032)
u rms = 482.8 m/s (rounded to three significant figures)
Therefore, the root mean speed of oxygen gas, O2, at 27.0°C is approximately 482.8 m/s.
To calculate the root mean speed of oxygen gas (O2) at 27.0 °C, we can use the formula for root mean square velocity (vrms):
vrms = √(3RT / M)
Where:
vrms = root mean speed (m/s)
R = gas constant = 8.314 Kg.m³/s².K.mol
T = temperature in Kelvin
M = molar mass (kg/mol)
First, let's convert the molar mass of oxygen (O2) from grams to kilograms:
Molar mass of O2 = 16 g/mol = 0.016 kg/mol
Next, let's convert the temperature from Celsius to Kelvin:
Temperature in Kelvin = 27.0 °C + 273.15 = 300.15 K
Now we can substitute the values into the formula and calculate the root mean speed (vrms):
vrms = √(3 * 8.314 * 300.15 / 0.016)
Calculating the expression within the square root:
vrms = √(7472.688/Kg.m³.s²)
Finally, calculating the square root:
vrms = 86.48 m/s
Therefore, the root mean speed of oxygen gas (O2) at 27.0 °C is approximately 86.48 m/s.