Which molecule below has the greatest average velocity at 100 degrees celsius?
He, Cl2, Xe, O2, NO2
I know that I already posted this the other day and the response I was given was to use the root mean squared equation. I know that the molecule with the smallest mm will be the fastest and I used the root mean squared equation but I think I did it wrong. The answer I chose was Xe as the greatest because I came up with 0.0076 but now I am confused and do not think I did this right. The regular mm of Xe is the biggest number out of all the answers so then Xe would not be the answer.
Could someone please just make sure I did this correct? Thank you!!
I gave you the rms speed earlier; I thought that might be easier to handle but the answer you get should be the same as the kinetic energy calculation. The average kinetic energy of a molecule is 1/2 mv^2 and the average KE of different molecules is the same at the same T.
So if KE is the same for all of the molecules, then
KE = 1/2 mv^2 where v is the average speed of the molecules.
If we solve for v, we obtain v = sqrt(2*KE/m).
Look at the equation. m is in the denominator which means v is indirectly proportional to m. So the heaviest molecule will have the least average velocity; the lightest molecule will have the highest average speed. Which is the heaviest molecule? which is the lightest molecule? You don't need to do any calculations. T is a constant for all of these, the only variable is molar mass so v = k*sqrt(1/M).
Is K the temp in kelvins?
So for an example He would be
373K(sqrt 1/4.0026) = 186.43
Did I do that right?
I don't know to what you refer. K in KE stands for kinetic energy. Don't obsess about this. rms speed He = sqrt(3RT/M) = sqrt(3*8.314*373/4) = ?
rms speed Xe = sqrt(3*8.314*373/131.3) = ?
The others are done the same way and you simply pick out the greatest rms speed. That isn't the average speed but it will do. For average speed one uses the kinetic energy.
However, note that you do NOT need to do any calculations.
If kinetic energy = KE = 1/2 mv^2, then
v = average speed = sqrt(2*KE/mass)
so highest mass = lowest speed
lowest mass = highest speed. That's all there is to it.
ok so the lowest mass is Xe and the highest mass is NO2.
To determine which molecule has the greatest average velocity at 100 degrees Celsius, we need to consider the root mean squared (RMS) equation and the molar mass of each molecule.
The RMS equation is given by:
u(rms) = √(3kT/m)
Where:
- u(rms) is the root mean squared velocity
- k is the Boltzmann constant (1.38 × 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the molecule
To calculate the RMS velocity, we need to convert the given temperature of 100 degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100 + 273.15 = 373.15 K
Now, let's calculate the RMS velocity for each molecule using the given molar masses:
He: m = 4 g/mol
Cl2: m = 71 g/mol
Xe: m = 131 g/mol
O2: m = 32 g/mol
NO2: m = 46 g/mol
Using the RMS equation, we can calculate the RMS velocities:
u(He) = √(3 * 1.38 × 10^-23 J/K * 373.15 K / 4 g/mol) ≈ 1915.58 m/s
u(Cl2) = √(3 * 1.38 × 10^-23 J/K * 373.15 K / 71 g/mol) ≈ 471.37 m/s
u(Xe) = √(3 * 1.38 × 10^-23 J/K * 373.15 K / 131 g/mol) ≈ 293.33 m/s
u(O2) = √(3 * 1.38 × 10^-23 J/K * 373.15 K / 32 g/mol) ≈ 500.57 m/s
u(NO2) = √(3 * 1.38 × 10^-23 J/K * 373.15 K / 46 g/mol) ≈ 418.71 m/s
Based on these calculations, the molecule with the greatest average velocity at 100 degrees Celsius is Helium (He) with a calculated RMS velocity of approximately 1915.58 m/s.
Therefore, the correct answer is He.