Question

A 15.0 L tank is filled with helium to a pressure of 2.00 * 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the temperature remains constant and that the tank cannot be emptied below 1.00 atm?

Answer 1

Answer:

1493 balloons.

Explanation:

Hello,

In this case, we first compute the total moles by temperature by using the ideal gas equation as shown below:

$n_{tot}=\frac{PV}{RT}=\frac{200atm*15.0L}{0.082\frac{atm*L}{mol*K}*T}=36585.4mol/T$

Moreover, since the tank cannot be emptied, we compute the moles that are not transferred:

$n_{not\ transferred}=\frac{1.00atm*15.0L}{0.082\frac{atm*L}{mol*K}*T}=182.93mol/T$

Now, we compute the moles that are actually transferred:

$n_{transferred}=36585.4mol/T-182.93mol/T=36402.5mol/T$

Next, since each balloon is filled up to 1.00 atm within a volume of 2.00 L, the moles per balloon are:

$n_{per\ balloon}=\frac{1.00 atm*2.00L}{0.082\frac{atm*L}{mol*K}*T}=24.39mol/T$

Then, the number of balloons are:

$balloons=\frac{n_{transferred}}{n_{per\ balloon}} =\frac{36402.5mol/T}{24.39mol/T}\\ \\balloons=1492.5\ balloons$

Which is more accurately 1493 balloons.

Regards.