Determine the fraction of the volume

[olso4142]

[SOLVED] Ideal Gases

Homework Statement

A gas has a temperature of 310K and a pressure of 101kPa (a.) find the volume occupied by 1.25 mol of this gas, assuming its ideal. (b.) assuming the gas molecules can be approximated as a small sphere of diameter 2.5x10^-10, determine the fraction of the volume found in part (a) that is occupied by the molecules.

Homework Equations

PV=nRT

The Attempt at a Solution

(a.) V=nRT/P
V= (1.25mol)(8.31J/mol*K)(310K)/0.101Pa
V= 31882.43 m^3

(b.)d= 2.5x10^-10
V(sphere)= 8.18x10^-30

n=PV/RT
n= (.101Pa)(31882.43m^3)/(8.31J/mol K)(310K)
n= 1.25 mol *6.022x10^23= 7.5275x10^23 molecules

do i just multiple these together and then find the fraction from the first volume?

 

[Chi Meson]

Yes, that works fine.

but notice, Vsphere/V can be determined without ever knowing n.

Since this fraction should not depend on how large your sample is, the number should "cancel out." solve for this fraction using variables (without plugging in numbers) and you will see n go away.

 

[rock.freak667]

For the first part...1kPa=1x10[itex]^3[/tex]Pa
and for the fraction occupied, vol.occupied by gas/vol.of sphere