Applying Charles's law and Boyle's law together, we can combine them into the ideal gas law:
PV = nRT
where:
* P = Pressure (mmHg)
* V = Volume (L)
* n = Number of moles (assumed constant)
* R = Gas constant (0.08206 L atm / K mol)
* T = Temperature (K)
We can rearrange the equation to find the final volume (V₂) at the new temperature (T₂) and pressure (P₂):
V₂ = V₁ * (T₂ / T₁) * (P₁ / P₂)
Plugging in the known values:
V₂ = 99.71 L * ((10.4 + 273.15) K / (44.7 + 273.15) K) * (707.2 mmHg / 602.6 mmHg)
V₂ ≈ 107.7 L
Therefore, the volume of the gas balloon at 10.4 °C and 602.6 mmHg would be approximately 107.7 liters.
