I had to find the root mean square velocity of a gas using the only formula KE=1/2MV^2 . Is this even possible using only this formula?
I have a text that starts with the basics and works up to total energy and finally to rms = sqrt(3RT/M). You might look on the web (Use google) to find a derivation.
The question is What is the root mean square velocity of ammonia molecules (NH3) at 45°C? -My teacher is telling me to use the formula KE=1/2MV^2 to find the velocity and told me to use 45 celcius as the KE and molar mass as M and solve for V^2. (45=17 * V2)
I thought KE is joules and not celcius so I'm confuse.
You're right. KE is in joules.
Your teacher may have been saying to use total KE = (3/2)*R*T and plug that into 1/2 mV^2.
If you do that
(3/2)RT = (1/2)mV^2
Plug 45 + 273 for T, R is 8.314. Use molar mass = 17 for m and solve for v (which is root mean square of the V term). If you do all of that notice that it gives you rms =sqrt(3RT/M). Your teacher just wants you to go the long route to see where that formula I gave you of of sqrt (3RT/M) comes from.
Yes, it is possible to find the root mean square (RMS) velocity of a gas using the kinetic energy formula KE = 1/2MV^2, where KE represents the kinetic energy, M is the molar mass of the gas, and V represents the velocity.
To find the RMS velocity, we can derive it from the kinetic energy formula. The kinetic energy of a gas is given by:
KE = 1/2MV^2
Since kinetic energy is directly proportional to the temperature (T) of the gas, we can also express KE in terms of T:
KE = (3/2)kT
Where k is the Boltzmann constant.
Since both expressions represent the same quantity (kinetic energy), we can equate them:
1/2MV^2 = (3/2)kT
Simplifying the equation:
V^2 = (3kT/M)
Taking the square root of both sides:
V = √(3kT/M)
This equation represents the RMS velocity of a gas. So, it is indeed possible to calculate the RMS velocity using the given kinetic energy formula, along with the knowledge of the molar mass (M) and temperature (T) of the gas.