Okay, let's think through this step-by-step:
* The temperature is -17 °C
* The air pressure is 0.700 atm
* The number of moles of gas in the balloon is 3.90 mol
* We want to find the volume of the gas
To find the volume, we can use the ideal gas law:
PV = nRT
Where:
P = Pressure (0.700 atm)
n = Number of moles of gas (3.90 mol)
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature in Kelvin (-17 °C + 273 = 256 K)
V = Volume (unknown)
Plugging in the values:
(0.700 atm)(V) = (3.90 mol)(0.0821 L·atm/mol·K)(256 K)
Solving this:
V = 261 L
Therefore, the volume of gas in the balloon is 261 L.