Consider the following entities: Ar, SiH3F, Xe and CClF3. which one will diffuse the fastest?what is rms speed (m/s) of the slowest moving atom at 25 C..?

The fastest diffuser is the one with the least mass. rms speed = sqrt(3RT/Molar mass)

thank you..

To determine which entity will diffuse the fastest, we need to compare their molar masses. The lighter the molar mass, the faster the particle will diffuse.

Let's calculate the molar masses of the given entities:

1. Ar (Argon):
Ar atomic mass = 39.95 g/mol

2. SiH3F (Silicon Trihydride Fluoride):
Si atomic mass = 28.09 g/mol
H atomic mass = 1.01 g/mol
F atomic mass = 18.99 g/mol
Molar mass of SiH3F = 28.09 g/mol + (3 x 1.01 g/mol) + 18.99 g/mol = 61.11 g/mol

3. Xe (Xenon):
Xe atomic mass = 131.29 g/mol

4. CClF3 (Trichlorofluoromethane):
C atomic mass = 12.01 g/mol
Cl atomic mass = 35.45 g/mol
F atomic mass = 18.99 g/mol
Molar mass of CClF3 = 12.01 g/mol + (3 x 35.45 g/mol) + 18.99 g/mol = 137.37 g/mol

Now, let's compare the molar masses:

Ar (39.95 g/mol) < SiH3F (61.11 g/mol) < Xe (131.29 g/mol) < CClF3 (137.37 g/mol)

Therefore, Ar will diffuse the fastest as it has the lowest molar mass.

To calculate the root mean square (rms) speed of the slowest moving atom at 25 °C, we can use the root mean square speed equation:

v = sqrt((3RT) / (M))

where:
v = rms speed
R = gas constant = 8.314 J/(mol*K)
T = temperature in Kelvin
M = molar mass in kg/mol

Given that the temperature is 25 °C, we need to convert it to Kelvin:

T = 25 °C + 273.15 = 298.15 K

Now, let's calculate the rms speed for Ar:

M(Ar) = 39.95 g/mol = 0.03995 kg/mol

Plug in the values into the equation:

v(Ar) = sqrt((3 * 8.314 J/(mol·K) * 298.15 K) / (0.03995 kg/mol))

v(Ar) ≈ 502.68 m/s

Therefore, the rms speed of the slowest moving Ar atom at 25 °C is approximately 502.68 m/s.

To determine which entity will diffuse the fastest, we need to consider the relative molecular weights and the presence of any intermolecular forces.

Diffusion is determined by the average velocity of the molecules or atoms. According to Graham's law of diffusion, the rate of diffusion is inversely proportional to the square root of the molar mass of the molecule or atom.

Let's calculate the molar masses for each entity:
Ar (Argon): 39.948 g/mol
SiH3F (Silicon trihydride fluoride): 47.093 g/mol
Xe (Xenon): 131.293 g/mol
CClF3 (Chlorotrifluoromethane): 104.456 g/mol

Now, let's calculate the square root of the molar masses:
√(Ar) ≈ 6.322 g/mol^0.5
√(SiH3F) ≈ 6.872 g/mol^0.5
√(Xe) ≈ 11.466 g/mol^0.5
√(CClF3) ≈ 10.220 g/mol^0.5

From these calculations, we can see that the entity with the lowest square root of the molar mass is Ar (Argon). Therefore, Ar will diffuse the fastest.

To calculate the RMS (root mean square) speed of the slowest moving atom, we can use the RMS speed formula:

v = √(3RT / m)

Where:
v represents the RMS speed
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin (25 °C = 25 + 273.15 = 298.15 K)
m is the molar mass in kg

Let's calculate the RMS speed for the slowest moving atom at 25 °C:

m (Ar) = 39.948 g/mol = 0.039948 kg/mol

Now, substituting the values into the formula:

v = √(3 * 8.314 J/(mol·K) * 298.15 K / 0.039948 kg)

By calculating this equation, you will determine the RMS speed of the slowest moving atom at 25 °C in meters per second (m/s).