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?
4 answers
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.
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.
1 answer