The density of nitrogen at STP is 1.25 kgm^-3. Find the r.m.s velocity of nitrogen molecule at 20 degree centigrade.
Vrms = sqrt [3RT/M]
M is the molar mass, 28 g/mol
R = 8.317*10^7 erg/mole K
T = 293 K
You don't need to know the the density, but you could use it to get R/M.
V will be in cm/s with these units
For some background on kinetic theory, see
http://itl.chem.ufl.edu/2041_f97/lectures/lec_d.html
To find the root mean square (r.m.s) velocity of a nitrogen molecule at 20 degrees Celsius, we can use the formula:
v = √((3kT) / m)
Where:
v = r.m.s velocity
k = Boltzmann constant (1.38 × 10^-23 J/K)
T = temperature in kelvin (20°C = 293 K)
m = mass of a nitrogen molecule
To find the mass of a nitrogen molecule, we need to know the molar mass of nitrogen (N₂). The molar mass of nitrogen is approximately 28 grams/mole.
Now, let's calculate the mass of a nitrogen molecule:
Mass of nitrogen molecule (m) = Molar mass / Avogadro's constant
m = (28 g/mol) / (6.022 × 10^23 molecules/mol)
Next, let's convert the density of nitrogen at STP into the quantity of nitrogen molecules in one cubic meter.
Density (ρ) = Mass / Volume
Mass = Density × Volume
We know that the density of nitrogen at STP (standard temperature and pressure) is 1.25 kg/m³.
To find the mass of nitrogen in one cubic meter, we multiply the density by the volume.
Mass = 1.25 kg/m³ × 1 m³ = 1.25 kg
Now, let's calculate the number of nitrogen molecules in one cubic meter:
Number of molecules = Mass / Mass of one molecule
Number of molecules = 1.25 kg / m
Now, we have the number of nitrogen molecules and the mass of one nitrogen molecule. So we can find the r.m.s velocity using the formula above.
v = √((3kT) / m)
v = √((3 × (1.38 × 10^-23 J/K) × 293 K) / (1.25 kg / (1.25 kg / m)))
Now, let's plug in the values and solve for the r.m.s velocity.