calculate the root mean square speed of nitrogen at 0 degree celcuis. Take the molecular weight of nitrogen M= 28*0.0010
To calculate the root mean square (rms) speed of a gas molecule, we can use the following formula:
rms speed = √((3 * k * T) / m)
Where:
- k is the Boltzmann constant (1.38 x 10^(-23) J/K)
- T is the temperature in Kelvin (0 degrees Celsius is equal to 273.15 Kelvin)
- m is the molecular mass of the gas
First, let's convert the temperature from Celsius to Kelvin:
T = 0 + 273.15
T = 273.15 K
Now, let's substitute the values into the formula:
rms speed = √((3 * k * T) / m)
rms speed = √((3 * 1.38 x 10^(-23) J/K * 273.15 K) / (28 * 0.0010 kg/mol))
For the molecular weight (M) of nitrogen given as 28 * 0.0010 kg/mol, we need to convert it to kg/particle by dividing it by Avogadro's number (6.022 x 10^23 particles/mol):
m = (28 * 0.0010 kg/mol) / (6.022 x 10^23 particles/mol)
m = 4.65 x 10^(-26) kg/particle
Now we can substitute the values into the formula:
rms speed = √((3 * 1.38 x 10^(-23) J/K * 273.15 K) / (4.65 x 10^(-26) kg/particle))
Calculating this, we find that the root mean square speed of nitrogen at 0 degrees Celsius is approximately 515.41 m/s.