What is the Most Probable Speed of a Gas at a Given Temperature?

[Romperstomper]

I'm having problems trying to figure out the most probable speed of a gas with the only givens being what gas it is and the temperature of the gas, for example, find the most probable speed of Ar at 127C. The equation is Ke = 1/2mv^2.

I know how to get the average kinetic energy, speed, and total kinetic energy. But, I'm stuck on how to get the most probable speed or energy with just these two pieces of information.

 

[zwtipp05]

I believe the equation for the average kinetic energy of a gas is $$\sqrt{kRT}$$
Where R is the ideal gas constant, T is temperature and k is Boltzmann's constant.

 

[Tide]

The probability of finding atoms with speeds between v and v + dv is proportional to $v^2 e^{-m v^2/{2 k_B T}}$ and you can find the most probable speed by setting its derivative to 0.