Question 5.2: A balloon is filled with helium, and its volume is 2.2 L at ......
A balloon is filled with helium, and its volume is 2.2 L at 298 K. The balloon is then dunked into a thermos bottle containing liquid nitrogen. When the helium in the balloon has cooled to the temperature of the liquid nitrogen (77 K), what will the volume of the balloon be?
Strategy We should start by recognizing this as a change in conditions for a gas and realize that we will want to use the ideal gas law. So we assume that the gas will behave ideally under both the initial and final conditions. We will further assume that the pressure is constant since we are not given any data to suggest otherwise. And since the balloon is tied off throughout, we can also assume that n is constant. Collect the constant terms together and work toward a solution.
As in the discussion above, we have
{\frac{V}{T}}={\frac{n R}{P}}= constant
So
{\frac{V_{1}}{T_{1}}}={\frac{V_{2}}{T_{2}}}
Solve this for the final volume (V_2):
V_{2}={\frac{V_{1}T_{2}}{T_{1}}}
Because the three terms on the right are known, we can just insert values and solve:
V_{2}={\frac{(2.2\,{\mathrm{L}})(77\,{\mathrm{K}})}{(298\,{\mathrm{K}})}}=0.57\,{\mathrm{L}}
Analyze Your Answer We have decreased the temperature from 298 K to 77 K, which means that it is smaller by a factor of nearly 4. This should lead to a volume that is also smaller by a factor of nearly 4. So our answer seems likely to be correct.
Check Your Understanding The balloon in the example above will burst if its volume exceeds 2.3 L. At what temperature would you expect the balloon to burst?