Final answer:
To find the most probable speed of nitrogen molecules at 233 K, use the Maxwell-Boltzmann distribution formula with Boltzmann's constant and the mass per nitrogen molecule obtained from the molar mass divided by Avogadro's number.
Step-by-step explanation:
The subject is looking to find the most probable speed (vp) of nitrogen molecules at a given temperature. The most probable speed can be calculated using the formula derived from the Maxwell-Boltzmann distribution:
vp = \sqrt{(2 \cdot k \cdot T) / m}
Where k is Boltzmann's constant (1.38 x 10-23 J/K), T is the temperature in kelvins, and m is the mass of one molecule of the gas.
To find the mass (m) of a nitrogen molecule (N2), we first convert the molar mass from grams per mole to kilograms per mole (28.0 g/mol becomes 28.0 x 10-3 kg/mol). Since one mole contains Avogadro's number of molecules (approximately 6.022 x 1023), we divide the molar mass by Avogadro's number to get the mass per molecule.
Molar mass of N2: 28.0 x 10-3 kg/mol
Mass per molecule: 28.0 x 10-3 kg/mol / 6.022 x 1023 molecules/mol
We then substitute the values into the equation to calculate vp.