Answer:
volume balloon 5.06 10⁻² m³
Explanation:
The balloon is inflated with air, which in the first instance behaves like an ideal gas, which has as an equation
PV = n R T
Where R is the ideal gas constant that is worth 8.314 J / mol K.
Let's use the initial data to calculate the number of moles of gas in the balloon that remains constant, but first we reduce all quantities to the SI system
V1 = 29.1 L (1 m2 / 1000 L) = 29.1 10⁻³ m³
P1 = 733 mmHg (1 105 Pa / 760 mmHg) = 0.964 10⁵ Pa
T1 = 24.7 + 273.15 = 297.85K
P2 = 365 mmHg (1 105 Pa / 760 mmHg) = 0.480 10⁵ Pa
T2 = -14.5 +273.15 = 258.65K
Let's clear and calculate the number of moles
n = P V / R T
n = P1 V1 / R T1
n = 0.964 10 5 29.1 10⁻³ / (8.314 297.85)
n = 1.13 moles
With the data of the second part we clear the volume and calculate
V = n R T / P
V2 = n R T2 / P2
V2 = 1.13 8.314 258.65 /0.480 10⁵
V2 = 5.062 10⁻² m³
