Find V rms and MM using density

[bmartz]

Homework Statement

At 332 K and 1.28 x 10^-2 atm, the density of a gas is 1.89 x 10^-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas.

Homework Equations

V_rms=√(3RT/M) (RMS speed)
PV=nRT (Ideal Gas Law)
D=m/V (Density)
M = m/n (Molar mass = mass/number of moles)

The Attempt at a Solution

Am I doing this wrong or is Wiley Plus wrong?

From Ideal Gas Law: V = nRT/P
Sub into Density: D = m/(nRT/P) = mP/nRT = (m/n)(P/RT)
Sub Molar mass: D = MP/RT
So M = DRT/P

Sub into RMS speed: V_rms = √(3RT/(DRT/P)) = √(3P/D)

After converting the pressure to Pa, and the density to kg/cm³, I got:
a) 4.53x10⁵ = 453000
b) 4.04x10^-3 = .0000000404

 

[jake929]

Homework Statement

At 332 K and 1.28 x 10^-2 atm, the density of a gas is 1.89 x 10^-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas.

Homework Equations

V_rms=√(3RT/M) (RMS speed)
PV=nRT (Ideal Gas Law)
D=m/V (Density)
M = m/n (Molar mass = mass/number of moles)

The Attempt at a Solution

Am I doing this wrong or is Wiley Plus wrong?

From Ideal Gas Law: V = nRT/P
Sub into Density: D = m/(nRT/P) = mP/nRT = (m/n)(P/RT)
Sub Molar mass: D = MP/RT
So M = DRT/P

Sub into RMS speed: V_rms = √(3RT/(DRT/P)) = √(3P/D)

After converting the pressure to Pa, and the density to kg/cm³, I got:
a) 4.53x10⁵ = 453000
b) 4.04x10^-3 = .0000000404

What does Wiley Plus say, does it show you are off by several orders of magnitude or the that your solution is wrong altogether? Your dimensional analysis of your solution yields velocity units. Which shows you should be on the right track, but your units are inconsistant. You converted pressure from atm to Pa(N/m^2). You converted density to kg/cm^3. To be consistent convert your density to kg/m^3. You'll get a different answer, how it compares to Wiley I don't 'know.

 

[ehild]

Hi bmartz,

Your equations for the RMS speed and molar mass are correct, but the results are wrong without the units. Check your units. What are they for the RMS speed and molar mass?

Also check if 4.04 x 10^-3 is really 0.0000000404?
ehild

 

[bmartz]

Sorry about that, units that I got:
a) m/s
b) kg

Also for b that was a typo, I meant to put in 4.04x10^-8.

 

[jake929]

V_rms=√(3RT/M)=√(J/(mole*K)*K*mole/kg)
moles cancel and Kelvin cancel giving √(J/kg)=√(kg*m²/(s²*kg))=m/s

your solution gives
√(3P/D)=√(Pa/(kg/cm³⁾)=√((N*cm³)/(m²*kg))
=√((kg*m*cm³)/(s²*m²*kg))
=√((cm³)/(s²*m)
in order to get m/s you need to convert cm³ to m³

 

[bmartz]

Thank you. Now I feel silly for missing that .