A container has a volume of #8 L# and holds #1 mol# of gas. If the container is expanded such that its new volume is #9 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

1 Answer
Jun 2, 2016

Answer:

#1.125# mol.

Explanation:

The law of the perfect gasses says:

#PV=nRT#

where #P# is the pressure, #V# is the volume, #n# is the number of mol #R# is the constant of the perfect gas and #T# is the temperature.

At the beginning #V_i=8# L and #n_i=1# mol while at the end #V_f=9# L. We want that all the quantities except #n# stay constant. So we can write the two equations such as

#PV_i=n_iRT#
#PV_f=n_fRT#

and we can divide the first for the second:

#\frac{PV_i}{PV_f}=\frac{n_iRT}{n_fRT}#

Only the quantities with index #i# or #f# changes, the other are constant, so we can cancel them

#V_i/V_f=n_i/n_f# and substituting the numbers

#8/9=1/n_f# and then

#n_f=9/8=1.125# mol.