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You have a 25.0 L cylinder of helium at a pressure of 132 atm and a temperature of 19 [infinity]C. The He is used to fill balloons to a volume of 2.50 L at 732 mm Hg and 27 [infinity]C. How many balloons can be filled with He? Assume that the cylinder can provide He until its internal pressure reaches 1.00 atm (i.e., there are 131 atmospheres of usable He in the cylinder).

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Answer: Number of balloons that can be filled with He are 1397.

Explanation:

The given data is as follows.

      V = 25 L He ,          P = 131 atm

      T = [tex]19^{o}C[/tex] = (19 + 273) K

          = 292 K

According to ideal gas equation,

            PV = nRT

where,     n = [tex]\frac{PV}{RT}[/tex]

                   = [tex]\frac{131 \times 25}{0.082 \times 292}[/tex]

                   = 136.76 mol of He

The data for small balloons is given as follows.

        T = [tex]27^{o}C[/tex] = (27 + 273) K

                   = 300 K

        P = 732 = 0.963 atm

        V = 2.50 L

Now, we will calculate the number of moles as follows.

       n = [tex]\frac{PV}{RT}[/tex]

          = [tex]\frac{0.963 \times 2.50}{0.082 \times 300}[/tex]

         = 0.098 mol

So, number of balloons that can be filled with He are calculated as follows.

         n = [tex]\frac{N_{1}}{N_{2}}[/tex]

            = [tex]\frac{136.76}{0.098}[/tex]

            = 1397.60 balloons

or,        = 1397 balloons (approx)

Thus, we can conclude that number of balloons that can be filled with He are 1397.

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