Final answer:
To find the volume of the helium-filled balloon at an altitude of 25 km, we can use the ideal gas law. First, we calculate the initial number of moles of helium at sea level. Then, using the new conditions at 25 km altitude, we can find the volume of the balloon. The volume is determined to be 123.65 L.
Step-by-step explanation:
To solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
Step 1: Convert the initial conditions (sea level) to Kelvin. The temperature is 20.0°C + 273.15 = 293.15 K and the pressure is 1 atm.
Step 2: Calculate the initial number of moles. We can use the ideal gas law to find n: n = PV/RT = (1 atm * 50.0 L) / (0.0821 L·atm/mol·K * 293.15 K) = 2.126 moles.
Step 3: Convert the new conditions (25 km) to Kelvin. The temperature is -35°C + 273.15 = 238.15 K and the pressure is 0.350 atm.
Step 4: Use the ideal gas law to find the volume at the new conditions: V = (n * R * T) / P = (2.126 moles * 0.0821 L·atm/mol·K * 238.15 K) / 0.350 atm = 123.65 L.
Therefore, the volume of the balloon at an altitude of 25 km is 123.65 L.