Answer:
[tex]\large \boxed{\text{3.9 L}}[/tex]
Explanation:
We can use the Combined Gas Laws to solve this problem
[tex]\dfrac{p_{1}V_{1} }{T_{1}} = \dfrac{p_{2}V_{2}}{T_{2}}[/tex]
Data
p₁ = 571.2 Torr; p₂ = 400 Torr
V₁ = 3.5 L; V₂ = ?
T₁ = 21.5 °C; T₂ = 6.8 °C
Calculations
(a) Convert the temperatures to kelvins
T₁ = (21.55 + 273.15) K = 294.70 K
T₂ = (6.8 + 273.15) K = 279.95 K
(b) Calculate the new volume
[tex]\begin{array}{rcl}\dfrac{p_{1}V_{1} }{T_{1}} & = & \dfrac{p_{2}V_{2}}{T_{2}}\\\\\dfrac{\text{571.2 Torr $\times$ 3.5 L}}{\text{294.65 K}} & = & \dfrac{\text{400 Torr} \times V_{2}}{\text{279.95 K}}\\\\\text{6.78 L} & = & \text{1.429V}_{2}\\\\V_{2} & = & \textbf{4.7 L}\\\end{array}\\\text{The new volume of the balloon is $\large \boxed{\textbf{4.7 L}}$}[/tex]
