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?

Answer 1

#1.125# mol.

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.
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Answer 2

To maintain a constant temperature and pressure, 1 mole of gas must be injected into the container.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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