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860 mL.
<h3>Explanation</h3>Separate this process into two steps:
- Cool the balloon from 305 K to 265 K.
- Reduce the pressure on the balloon from 0.45 atm to 0.25 atm.
What would be the volume of the balloon after each step?
After Cooling the balloon at constant pressure:
By Charles's Law, the volume of a gas is directly related to its temperature in degrees Kelvins.
In other words,
,
where
and
are volumes of the same gas.
and
are the temperatures (in degrees Kelvins) of that gas.
Rearranging,
.
The balloon ended up with a lower temperature. As a result, its volume drops: .
After reducing the pressure on the balloon at constant temperature:
By Boyle's Law, the volume of a gas is inversely proportional to the pressure on this gas.
In other words,
,
where
and
are the pressures on this gas.
Rearranging,
.
There's now less pressure on the balloon. As a result, the balloon will gain in volume: .
The final volume of the balloon will be .