Final answer:
Using the Ideal Gas Law, we find that a balloon filled with 2.50 moles of gas at 24°C and a pressure of 1.78 atm has a volume of approximately 34.82 liters.
Step-by-step explanation:
To find the volume of the balloon filled with gas, we can use the Ideal Gas Law which can be stated as PV = nRT, where:
- P is the pressure of the gas,
- V is the volume of the gas,
- n is the amount of substance of the gas (in moles),
- R is the ideal, or universal, gas constant,
- T is the temperature of the gas (in Kelvin).
Given that:
- P = 1.78 atm,
- n = 2.50 moles,
- T = 24°C = 297 K (since we must convert to Kelvin: T(K) = T(°C) + 273.15),
- R = 0.0821 L·atm/K·mol (universal gas constant).
Inserting these values into the Ideal Gas Law equation:
(1.78 atm) x V = (2.50 mol) x (0.0821 L·atm/K·mol) x (297 K)
Now isolate V for the volume:
V = ((2.50 mol) x (0.0821 L·atm/K·mol) x (297 K)) / (1.78 atm)
After calculating, the volume V ≈ 34.82 liters.