A container has a volume of #2 L# and holds #1 mol# of gas. If the container is expanded such that its new volume is #8 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Answer 1

4 moles of gas must be injected into the container.

Let's use Avogadro's law:

#v_1/n_1 = v_2/n_2#

The number 1 represents the initial conditions and the number 2 represents the final conditions.

• Identify your known and unknown variables:

#color(blue)("Knowns:"# #v_1#= 2 L #v_2#= 8 L #n_1#= 1 mol
#color(magenta) ("Unknowns:"# #n_2#

• Rearrange the equation to solve for the final number of moles:

#n_2=(v_2xxn_1)/v_1#

• Plug in your given values to obtain the final number of moles:

#n_2=(8 cancelLxx1mol)/(2\cancel"L")# = # 4 mol#
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Answer 2

According to Avogadro's law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. Therefore, to maintain the same temperature and pressure when the volume increases from 2 L to 8 L, the number of moles of gas must also increase proportionally.

Using the equation:

(Volume 1 / Moles 1) = (Volume 2 / Moles 2),

and plugging in the given values:

(2 L / 1 mol) = (8 L / x mol),

we can solve for x to find the number of moles of gas needed for the new volume.

2 L / 1 mol = 8 L / x mol, 2x = 8, x = 4 moles.

Therefore, 4 moles of gas must be injected into the container to maintain a constant temperature and pressure.

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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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