Question

A 202 L tractor tire is filled up in the morning at a temperature of 15.1 degree celcius to a gauge pressure of 35.3 psi. By afternoon the temperature increases by 15.7 degree celcius, the gauge pressure increases by 2 psi, but the volume decreases to 94% of it original value. Use the ideal gas law to find out how many molecules leaked out.

Show work and answer for points.

Answer 1

First determine the number of moles in the morning,

PV=nRT

P_morn = 35.3 psi converted to atms using 1 psi = .06804 atm (found online) 37.3 psi * .06804 atm/1psi = 2.4 atm

V= 202

R= .0821 constant for atms

T = (273 + 15.1) = 288.1 K Converted C to K by adding C to 273

n = PV/RT = (2.4)(202)/[(.0821)(288.1)] = 20.496 mols in the morning

Then determine mols later,

P = 37.3 psi = 2.53 atm

V= 202(.94) = 189.88 L

T= 288.7

n = PV/RT = (2.53)(189.88)/[(.0821)(288.7)] = 20.268

Then subtract the moles from each time (n morning - n afternoon) This gives the total number of moles that escaped.

20.496-20.268 = .228 moles escaped

Now convert mols to molecules using 1 mole = 6.022 x 10²³ molecules

.228 mol x 6.022 x 10²³/1 mol = 1.37 x 10²³ molecules of gas escaped