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A #4.60L# volume of gas at #845mmHg# pressure is expanded such that the new pressure is #368mm*Hg#. To what volume does it expand?

Answer 1

Wyatt Atkins

A measurement of #845*mm*Hg# is illegitimate.......

See this old question.......

To solve this question we would use.....

#V_2=(P_1V_1)/P_2#, but we would insist on kosher units.......

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Answer 2

Noah Aldrich

#V_2 = 10.6# #"L"#

NOTE: Ideally, measurements of pressures greater than #760# #"mm Hg"# are non-ideal, because mercury barometers only measure up to that value. The equivalent unit, the #"torr"#, should be used if the pressure value exceeds #760# #"mm Hg"#.

We're asked to find the volume necessary for a gas system to exert a pressure of #368# #"mm Hg"#, assuming no change in temperature or amount of gas.

To do this, we can use the pressure-volume relationship of gases illustrated by Boyle's law:

#ulbar(|stackrel(" ")(" "P_2V_1 = P_2V_2" ")|)" "# (constant temperature and quantity)

where

#P_1# and #P_2# are the initial and final pressures of the gas, respectively

#V_1# and #V_2# are the inital and final volumes of the gas, respectively

We know:

#P_1 = 845# #"mm Hg"#

#V_1 = 4.60# #"L"#

#P_2 = 368# #"mm Hg"#

#V_2 = ?#

Let's rearrange the equation to solve for the final volume, #V_2#:

#V_2 = (P_1V_1)/(P_2)#

Plugging in known values:

#color(red)(V_2) = ((845cancel("mm Hg"))(4.60color(white)(l)"L"))/(368cancel("mm Hg")) = color(red)(ulbar(|stackrel(" ")(" "10.6color(white)(l)"L"" ")|)#

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Answer 3

Wyatt Atkins

Using Boyle's Law, we can calculate the final volume of the gas:

$P_1V_1 = P_2V_2$

Where:
$P_1 = 845\ mmHg$ (initial pressure)
$V_1 = 4.60\ L$ (initial volume)
$P_2 = 368\ mmHg$ (final pressure)
$V_2 = ?$ (final volume)

Plugging in the values:

$845\ mmHg \times 4.60\ L = 368\ mmHg \times V_2$

Solving for $V_2$ :

$V_2 = \frac{845\ mmHg \times 4.60\ L}{368\ mmHg} = 10.59\ L$

So, the gas expands to a final volume of $10.59\ L$ .

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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.

A #4.60*L# volume of gas at #845*mm*Hg# pressure is expanded such that the new pressure is #368*mm*Hg#. To what volume does it expand?

A #4.60L# volume of gas at #845mmHg# pressure is expanded such that the new pressure is #368mm*Hg#. To what volume does it expand?