What is the root-mean-square speed of N2O at 25°C?
u(rms) = sqrt(3RT/M)
M is molar mass
To find the root-mean-square (rms) speed of N2O at 25°C, we can use the following formula:
vrms = √((3 * R * T) / M)
Where:
vrms is the root-mean-square speed
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
M is the molar mass
First, let's convert the temperature from Celsius to Kelvin:
T (Kelvin) = T (Celsius) + 273.15
So, T = 25 + 273.15 = 298.15 K
Next, we need to calculate the molar mass of N2O (dinitrogen monoxide or nitrous oxide).
The molar mass of N2O is:
M (N2O) = (2 * M (N)) + M (O)
where M (N) is the molar mass of nitrogen and M (O) is the molar mass of oxygen.
The molar mass of nitrogen (N) is approximately 14.01 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.
Therefore,
M (N2O) = (2 * 14.01) + 16.00 = 44.02 g/mol
Now, substitute the values into the formula:
vrms = √((3 * R * T) / M)
vrms = √((3 * 8.314 * 298.15) / 44.02)
vrms ≈ √12408.73 / 44.02
vrms ≈ √281.88
vrms ≈ 16.79 m/s (rounded to two decimal places)
The root-mean-square speed of N2O at 25°C is approximately 16.79 m/s.