To determine the volume of the balloon at a different temperature while keeping the pressure constant, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature at constant pressure.
Charles's Law can be mathematically expressed as:
V₁ / T₁ = V₂ / T₂
Where: V₁ is the initial volume of the balloon (2500.0 mL) T₁ is the initial temperature (30.0 °C + 273.15 = 303.15 K) [converted to Kelvin] V₂ is the final volume of the balloon (unknown) T₂ is the final temperature (10.0 °C + 273.15 = 283.15 K) [converted to Kelvin]
Using the formula and substituting the values, we can solve for V₂:
2500.0 mL / 303.15 K = V₂ / 283.15 K
V₂ = (2500.0 mL / 303.15 K) * 283.15 K
V₂ ≈ 2335.45 mL
Therefore, the volume of the balloon at a temperature of 10.0 °C will be approximately 2335.45 mL.