Question

7. A gas-filled weather balloon with a volume of 65.0 L is released at sea-level conditions of

Answer 1

The balloon will reach its maximum volume and it will burst.

Given:

• A weather balloon at sea level, with gas at 65.0 L volume, 745 Torr pressure, and 25C temperature.
• When the balloon was taken to an altitude at which temperature was 25C and pressure was 0.066atm its volume expanded.
• The maximum volume of the weather balloon is 835 L.

To find:

Whether the weather balloon will reach its maximum volume or not.

Solution:

The pressure of the gas in the weather balloon at sea level = $P_1=745 torr$

$1 atm = 760 torr\\P_1=745 torr=\frac{745}{760} torr = 0.980 atm$

The volume of the weather balloon at sea level = $V_1=65.0L$

The temperature of the gas in the weather balloon at sea level:

$T_1=25^oC=25+273.15 K=298.15 K$

The balloon rises to an altitude.

The pressure of the gas in the weather balloon at the given altitude:

$P_2=0.066atm$

The volume of the weather balloon at the given altitude = $V_2=?$

The temperature of the gas in the weather balloon at the given altitude:

$T_1=25^oC=25+273.15 K=298.15 K$

Using the Combined gas law:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\\frac{0.980 atm\times 65.0L}{298.15 K}=\frac{0.066atm\times V_2}{298.15K}\\V_2=\frac{0.980 atm\times 65.0L\times 298.15K}{0.066atm\times 298.15 K}\\=965L$

The maximum volume of the weather balloon= V = 835 L

$V < V_2$

The volume of the weather balloon at a given altitude is greater than its maximum volume which means the balloon will reach its maximum volume and it will burst.

Learn more about the combined gas law:

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