Calculate the rms speed of NF3 molecules at 27 ∘C.
rms = sqrt(3RT/M) where M is molar mass.
The root-mean-square (rms) speed of gas molecules can be calculated using the following formula:
v = √(3RT/M)
Where:
v is the rms speed
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
M is the molar mass of the gas in kg/mol
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
Substituting the values:
T(K) = 27 + 273.15
T(K) = 300.15 K
The molar mass of NF3 can be calculated as follows:
M(NF3) = (M(N) * 1) + (M(F) * 3)
Looking up the molar masses of nitrogen (N) and fluorine (F) from the periodic table:
M(N) = 14.007 g/mol
M(F) = 18.998 g/mol
M(NF3) = (14.007 g/mol * 1) + (18.998 g/mol * 3)
M(NF3) = 14.007 g/mol + 56.994 g/mol
M(NF3) = 71.001 g/mol
Converting the molar mass from grams to kilograms:
M(NF3) = 71.001 g/mol / 1000
M(NF3) = 0.071001 kg/mol
Now we can substitute these values into the formula to calculate the rms speed:
v = √(3 * R * T / M)
v = √(3 * 8.314 J/(mol·K) * 300.15 K / 0.071001 kg/mol)
v = √(37375.3582 J/(mol·K) / 0.071001 kg/mol)
v = √(527,012.898 mol^2·J / kg)
v = √(527,012.898 m^2·s^-2)
v = 726.39 m/s
Therefore, the rms speed of NF3 molecules at 27 °C is approximately 726.39 m/s.
To calculate the root mean square (rms) speed of NF3 (nitrogen trifluoride) molecules at 27 °C, we can use the formula:
v rms = √((3 * k * T) / m)
where:
- v rms is the rms speed
- k is the Boltzmann constant (1.38 * 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of NF3 (in kg/mol)
First, let's convert the given temperature from Celsius to Kelvin:
T = 27 °C + 273.15 = 300.15 K
Next, we need to determine the molar mass of NF3. Adding up the atomic masses, we have:
- Nitrogen (N) = 14.01 g/mol
- Fluorine (F) = 18.99 g/mol
Molar mass of NF3 = (3 * 18.99 g/mol) + 14.01 g/mol = 71.97 g/mol
Now, we need to convert the molar mass from grams to kilograms:
m = 71.97 g/mol / 1000 g/kg = 0.07197 kg/mol
Finally, we can substitute the values into the formula:
v rms = √((3 * 1.38 * 10^-23 J/K * 300.15 K) / 0.07197 kg/mol)
Calculating this expression will give you the rms speed of NF3 molecules at 27 °C.