The volume of the balloon is approximately 2652 liters.
How to determine the volume occupied by the gas in a balloon
Let suppose that flammable hydrogen behaves ideally. GIven the molar mass ([tex]M[/tex]), in kilograms per kilomole, and mass of the gas ([tex]m[/tex]), in kilograms. The volume occupied by the gas ([tex]V[/tex]), in cubic centimeters, is found by the equation of state for ideal gases:
[tex]V = \frac{m\cdot R_{u}\cdot T}{P\cdot M}[/tex] (1)
Where:
- [tex]R_{u}[/tex] - Ideal gas constant, in kilopascal-cubic meters per kilomole-Kelvin.
- [tex]T[/tex] - Temperature, in Kelvin
- [tex]P[/tex] - Pressure, in kilopascals
If we know that [tex]m = 0.239\,kg[/tex], [tex]R_{u} = 8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K}[/tex], [tex]T = 273.15\,K[/tex], [tex]P = 101.325\,kPa[/tex] and [tex]M = 2.02\,\frac{kg}{kmol}[/tex], then the volume of the balloon is:
[tex]V = \frac{(0.239\,kg)\cdot \left(8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K} \right)\cdot (273.15\,K)}{\left(101.325\,kPa\right)\cdot \left(2.02\,\frac{kg}{kmol} \right)}[/tex]
[tex]V = 2.652\,m^{3}[/tex] ([tex]2652\,L[/tex])
The volume of the balloon is approximately 2652 liters. [tex]\blacksquare[/tex]
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