Final answer:
To fill a 3.00 L flask with a total pressure of 2.00 atm at 298 K with a mixture of hydrogen and oxygen, approximately 4.512 g of water must decompose. The ideal gas law is used to calculate the number of moles of the mixture, and the balanced chemical equation is used to determine the number of moles of oxygen produced.
Step-by-step explanation:
To determine the mass of water that must decompose to fill a 3.00 L flask with a total pressure of 2.00 atm at 298 K with a mixture of hydrogen and oxygen, we can use the ideal gas law. The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to calculate the number of moles of the mixture from the ideal gas law equation. We know that the total pressure is 2.00 atm, the volume is 3.00 L, the temperature is 298 K, and the ideal gas constant (R) is 0.08206 L·atm/mol·K. Rearranging the ideal gas law equation to solve for n, we have:
n = (PV)/(RT) = (2.00 atm * 3.00 L)/(0.08206 L·atm/mol·K * 298 K) = 0.249 mol
Since the balanced chemical equation for the decomposition of water is 2H2O → 2H2 + O2, we know that for every 2 moles of water, we get 1 mole of oxygen. Therefore, the number of moles of oxygen produced is half of the number of moles of water decomposed, which is 0.249 mol / 2 = 0.1245 mol.
To calculate the mass of water, we can use the molar mass of water (H2O), which is 18.015 g/mol. The mass of water required to decompose is therefore 0.249 mol * 18.015 g/mol = 4.512 g.