Final answer:
To find the volume of a balloon containing 3.2 moles of helium at 65 degrees Celsius and a pressure of 2.0 atmospheres, we use the Ideal Gas Law PV = nRT. After converting the temperature to Kelvin and plugging in the known values into the equation, we determine the volume is 45 liters.
Step-by-step explanation:
The volume of a balloon containing helium can be determined using the Ideal Gas Law, which follows the formula PV = nRT. Here, 'P' represents the pressure of the gas, 'V' is the volume, 'n' is the number of moles, 'R' is the ideal gas constant, and 'T' is the temperature in Kelvin. To find the volume of a balloon with 3.2 moles of helium at a temperature of 65 degrees Celsius (which converts to 338 K) and a pressure of 2.0 atmospheres, the following steps are taken:
- Convert the Celsius temperature to Kelvin by adding 273 to the Celsius temperature: 65 °C + 273 = 338 K.
- Use the Ideal Gas Law formula: V = (nRT)/P.
- Plug in the values: V = (3.2 moles × 0.0821 L·atm/K·mol × 338 K) / 2.0 atm.
- Calculate: V = (3.2 × 0.0821 × 338) / 2 = 45 liters (rounded to two decimal places).
The volume of the balloon under the given conditions is 45 liters.