Final answer:
Approximately 0.40 moles of H2 gas are required to fill a 9.00-liter balloon at standard temperature and pressure (STP).
Step-by-step explanation:
To determine how many moles of H2 gas are needed to fill a 9.00-liter balloon, we can use the Ideal Gas Law, which is PV = nRT. Here 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. Assuming that the balloon is filled at standard temperature and pressure (STP), where P = 1 atm and T = 273.15 K, and the value of R is 0.0821 L·atm/(mol·K), we can rearrange the equation to solve for n (moles of gas).
n = PV / (RT)
Under STP conditions, we substitute P = 1 atm, V = 9.00 L, R = 0.0821 L·atm/(mol·K), and T = 273.15 K into the equation:
n = (1 atm × 9.00 L) / (0.0821 L·atm/(mol·K) × 273.15 K)
After calculating, the answer comes out to approximately 0.40 moles of H2 gas needed to fill the balloon.