A large balloon is initially filled to a volume of 25.0 L at 353 K and a pressure of 2575 mm Hg. What volume of gas will the bal

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loon contain at 1.35 atm and 253 K?

1 answer:

Tems11 [2.7K] · Answer 1 · 2026-02-26T12:04:19+03:00

Answer:

A balloon will hold a gas volume of 45.0 L at a pressure of 1.35 atm and a temperature of 253 K.

Explanation:

Applying the Ideal Gas Law for the same gas amount, we have:

$\frac {{P_1}\times {V_1}}{T_1}=\frac {{P_2}\times {V_2}}{T_2}$

Parameters are given as follows:

V₁ = 25.0 L

V₂ =?

P₁ = 2575 mm Hg

To convert pressure to atmospheres: P (atm) = P (mm Hg) / 760

P₁ = 2575 / 760 atm = 3.39 atm

P₂ = 1.35 atm

T₁ = 353 K

T₂ = 253 K

Using the earlier formula, we derive:

$\frac {{P_1}\times {V_1}}{T_1}=\frac {{P_2}\times {V_2}}{T_2}$

$\frac{{3.39}\times {25.0}}{353}=\frac{{1.35}\times {V_2}}{253}$

$\frac{1.35V_2}{253}=\frac{3.39\times \:25}{353}$

By solving for V₂, we find:

V₂ = 45.0 L

A balloon will hold a gas volume of 45.0 L at a pressure of 1.35 atm and a temperature of 253 K.