Final answer:
To calculate the volume of the balloon filled with hydrogen gas, first we find the number of moles of H2 (129.7 moles), then use the Ideal Gas Law, resulting in a balloon volume of 29,240 liters.
Step-by-step explanation:
The student's question involves calculating the volume of a balloon filled with hydrogen gas at a specific temperature and pressure using the Ideal Gas Law. The Ideal Gas Law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin. Given that there are 262 g of H2 and the molar mass of H2 is 2.02 g/mol, the first step is to calculate the number of moles of H2:
n = mass / molar mass n = 262 g / (2.02 g/mol) n = 129.7 moles
Now that we have the number of moles, we use the Ideal Gas Law to find the volume:
PV = nRT V = nRT / P
To proceed, we must ensure all units are in the correct form. The pressure is 1 atm, which can be used directly in the calculation; however, the temperature needs to be converted from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15 T(K) = 0°C + 273.15 = 273.15 K
The universal gas constant R is typically 0.0821 L·atm/(mol·K). Plugging in the values:
V = (129.7 moles) * (0.0821 L·atm/(mol·K)) * (273.15 K) / (1 atm)
V = 29,240 L
Therefore, the volume of the balloon is 29,240 liters.