Calculation of average molecular speed

[subhradeep mahata]

Homework Statement

Calculate the average speed of 2 mol oxygen molecules at pi*10bar pressure occupying 8 litres volume.

Relevant Equations

Given in the "Attempt at a Solution" section

We can calculate the average speed using this formula: u_avg=root(8PV/ΠnM)
I plugged in the following values:
P= pi*10 atm (bar is approximately equal to atm)
V=8lts
n=2mol
M=32*10^^-3kg/mol
But it is giving wrong answer. Can you tell me what went wrong?

 

[HallsofIvy]

Is this a joke or do you just want someone to do your homework for you? You ask "what went wrong" but don't show what you did nor what answer you got!

 

[mjc123]

Units?

 

[subhradeep mahata]

@HallsofIvy Actually I am pretty sure that I plugged in values having wrong units, that's why I just showed the values and what formula I am using. I just wanted to know what units are to be used in the formula.

 

[subhradeep mahata]

@mjc123 Yeah probably. Can you tell me what units should I use?

 

[mjc123]

Consistent ones. I would convert everything to SI units.

The one thing you must never do is blindly plug numbers into a formula without consideration of units, e.g. mixing atm, L, kg etc. (some SI and some not).

 

[Charles Link]

Suggest you use SI units. The pressure $P$ needs to be in $Newton/m^2$. $\\$ The formula you have comes from $\bar{v}=\sqrt{\frac{8 k_bT}{\pi m}}$, where $m$ is the mass of the molecule or atom. $\\$ Meanwhile, with the ideal gas law $PV=n R T=N k_b T$, where $N=$ number of molecules, so that $N=n N_A$ where $n =$ number of moles, and $N_A=$ Avagadro's number, we can write $\bar{v}=\sqrt{\frac{8 PV}{\pi n M}}$, where $M=m N_A$, is the mass of a mole of atoms or molecules.