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a balloon with a final volume of 12.0 L reduced it's pressure to 0.5 atmosphere without a change in temperature. What was the Balloon's initial pressure if it has 2.0L of gas before?



Answer :

Despina

Answer:

  • [tex]{\large{\boxed{3 \ atm }}} [/tex]

Explanation:

Using Boyle's Law : the pressure of a gas is inversely proportional to its volume when temperature is constant.

[tex] P_1 V_1 = P_2 V_2 [/tex]

Where, [tex] P_1 [/tex] & [tex]V_1[/tex] are inital pressure and initial volume

[tex]P_2[/tex] & [tex]V_2[/tex] are final pressure and final volume

Given, a balloon with a final volume of 12.0 L reduced it's pressure to 0.5 atmosphere without a change in temperature.

Here,

  • [tex]P_2 = 0.5 \: atm[/tex]
  • [tex]V_2 = 12.0 \: L [/tex]

We need to find the balloon's initial pressure if it has 2.0l of gas before :

  • [tex]P_1 = ? [/tex]
  • [tex]V_1 = 2.0 \: L [/tex]

Plugging in the given values :

[tex]P_1 \times 2.0 L = 0.5 \: atm \times \: 12.0 \: L[/tex]

[tex]P_1 = 0.5 \: atm \times 12.0 \: L / 2.0 \: L[/tex]

[tex]P_1 = 3.0 \: atm[/tex]

Therefore, the initial pressure of the balloon is 3 atm