Final answer:
To find the moles of nitrogen gas needed, we first calculate the pressure contributed by the existing oxygen gas using the ideal gas law, then solve for the number of moles of nitrogen that would contribute the pressure needed to reach the total desired pressure.
Step-by-step explanation:
To determine how many moles of nitrogen gas must be added to a 12.0 L flask containing 4.25 mol of oxygen gas at 15ºC to achieve a total pressure of 10.0 atm, we can use the ideal gas law: PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is temperature in Kelvin.
First, we convert 15ºC to Kelvin by adding 273.15 to get 288.15 K.
Next, we calculate the partial pressure contributed by the oxygen using its moles and the ideal gas law, remembering that R is 0.0821 L·atm/K·mol:
Oxygen's partial pressure (Po2) = (moles of O₂) × R × T / V
Po2 = (4.25 mol) × (0.0821 L·atm/K·mol) × (288.15 K) / (12.0 L)
Now that we have the pressure of oxygen, we subtract it from the desired total pressure to find the pressure that nitrogen must contribute.
Finally, using the pressure that nitrogen must contribute, we apply the ideal gas law again to solve for the moles of nitrogen needed.
We can use the examples provided for reference, applying the same principles to find the total number of moles in a mixture of gases or to calculate partial pressures when given total pressure and moles of components.