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The manufacturer specs for a particular balloon indicate the maximum inflated volume is 3.00 L. The balloon is filled with 2.50 L of helium at sea level (assume P= 1.00 atm) and released. When the balloon rises to a higher altitude where the pressure is 450.0 mm Hg, will the balloon burst? Show a calculation to support your answer. Assume constant temperature.

Respuesta :

Answer: The balloon will burst as it occupies higher volume than  maximum inflated volume.

Explanation:

To calculate the new volume, we use the equation given by Boyle's law. This law states that pressure is inversely proportional to the volume of the gas at constant temperature.  

The equation given by this law is:

[tex]P_1V_1=P_2V_2[/tex]

where,

[tex]P_1[/tex] = initial pressure of gas= 1.00 atm = 760.0 mm Hg  

[tex]V_1[/tex] =  initial volume of gas = 2.50 L

[tex]P_2[/tex] = final pressure of gas= 450.0 mm Hg

[tex]V_2[/tex] = final volume of gas = ?

Putting values in above equation, we get:

[tex]760.0\times 2.50=450.0\times V_2[/tex]

[tex]V_2=4.22L[/tex]

Thus the final volume of the gas is 4.22 L and as the maximum inflated volume is 3.00 L, the balloon will burst.

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