Homework Problem regarding speed of hydrogen molecule

[Mr. Goosemahn]

Homework Statement

You place 83 moles of hydrogen gas in a balloon of volume 2.8 m3, and find the pressure to be 1.4 times atmospheric pressure. What is the typical speed of a hydrogen molecule?

Homework Equations

v=(sqrt)((3*Boltzmann Constant*T)/m_hydrogen

T=pv/nr

The Attempt at a Solution

I plugged in the values I had:

v=(sqrt)((3*(1.3806503*10^-23)*575*2.8)/1.67372354 × 10-27)

This doesn't work, though.

What's wrong in this procedure?

 

[ideasrule]

v=(sqrt)((3*(1.3806503*10^-23)*575*2.8)/1.67372354 × 10-27)

This doesn't work, though.

What's wrong in this procedure?

Where did the 2.8 come from: Your equation was:

v=(sqrt)((3*Boltzmann Constant*T)/m_hydrogen

 

[stanton]

kinetic energy is related to typical speed. We know that the typical speed is proportional to temperature.
So first you should find the temperature using the ideal gas law.

When temperature is known, use the average translational kinetic energy of a molecule:
(3/2)k*T where k = Boltzmann's constant.
Set this equal to (1/2)mv^2 which is the formula for KE using:
m = mass of a hydrogen molecule to find v.
m is given as 83moles.

 

[ideasrule]

The OP has already found the temperature as well as the correct formula for v. He also found the right value for "m", which isn't 83 moles; it's 1.67e-27 kg. The only problem with his solution is that he has an extra 2.8 in there.