Consider the following: CH4, SiH3Cl, Ar, and CH2F2.
(a) Which one will diffuse the fastest?
(b) What is the rms speed (m/s) of the slowest-moving atom or molecule at 25°C?
a)
The fastest diffuser is the loest molar mass substance.
b)
urms = sqrt(3RT/M)
M is molar mass. R is 8.314. T in kelvin.
To determine which molecule will diffuse the fastest, we need to compare their molar masses. The lighter the molecule, the faster it will diffuse.
(a) Let's compare the molar masses of the molecules:
- CH4 (methane) has a molar mass of 12.01 g/mol + 4 * 1.01 g/mol = 16.05 g/mol.
- SiH3Cl (chlorosilane) has a molar mass of 28.09 g/mol + 3 * 1.01 g/mol + 35.45 g/mol = 62.56 g/mol.
- Ar (argon) has a molar mass of 39.95 g/mol.
- CH2F2 (difluoromethane) has a molar mass of 12.01 g/mol + 2 * 19.00 g/mol + 2 * 1.01 g/mol = 66.03 g/mol.
Comparing the molar masses, we see that Ar has the lowest molar mass (39.95 g/mol), so it will diffuse the fastest. Therefore, Ar will diffuse the fastest among the given molecules.
(b) To calculate the root-mean-square (rms) speed of the slowest-moving atom or molecule at 25°C, we can use the following equation:
v = sqrt((3 * R * T) / M)
Where:
- v is the rms speed (m/s)
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (25°C = 298 K)
- M is the molar mass of the molecule in kg/mol.
Let's calculate the rms speed for the slowest-moving atom or molecule.
The slowest-moving atom is Ar, with a molar mass of 39.95 g/mol = 0.03995 kg/mol.
Plugging these values into the equation, we get:
v = sqrt((3 * 8.314 J/(mol·K) * 298 K) / 0.03995 kg/mol)
Calculating the final result will give us the rms speed of the slowest-moving atom or molecule.