Final answer:
To calculate the volume of the balloon filled with hydrogen gas, we can use the ideal gas law equation: PV = nRT. Rearranging the equation and plugging in the given values, we find that the volume is 84.3 m³.
Step-by-step explanation:
To calculate the volume of the balloon, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. First, we need to convert the temperature from Celsius to Kelvin by adding 273.15 to it, so the temperature becomes 295.05 K. Next, we can rearrange the ideal gas law to solve for V: V = (nRT)/P. Plugging in the values, we have V = (0.400 mol)(8.314 m³·Pa/mol·K)(295.05 K)/(1.20 Pa). Calculating this, we find that the volume of the balloon is 84.3 m³.