A 21 L cylinder containing helium gas at a pressure of 47.9 atm is used to fill a weather balloon in order to lift equipment int
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6.52 × 10⁴ L. (3 sig. fig.)
<h3>Explanation</h3>Helium is a noble gas. The interaction between two helium molecules is rather weak, which makes the gas rather "ideal."
Consider the ideal gas law:
,
where
is the pressure of the gas,
is the volume of the gas,
is the number of gas particles in the gas,
is the ideal gas constant, and
is the absolute temperature of the gas in degrees Kelvins.
The question is asking for the final volume of the gas. Rearrange the ideal gas equation for volume:
.
Both the temperature of the gas, , and the pressure on the gas changed in this process. To find the new volume of the gas, change one variable at a time.
Start with the absolute temperature of the gas:
,
.
The volume of the gas is proportional to its temperature if both and
stay constant.
- consider
.
Now, keep the temperature at and change the pressure on the gas:
,
.
The volume of the gas is proportional to the reciprocal of its absolute temperature if both
and
stays constant. In other words,
(3 sig. fig. as in the question.).
See if you get the same result if you hold constant, change
, and then move on to change
.