To solve this problem, we can use the ideal gas law, which states that 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.
Since the pressure and temperature are constant, we can simplify the equation to V1/n1 = V2/n2, where V1 is the initial volume, n1 is the initial number of moles, V2 is the final volume, and n2 is the final number of moles.
Given: Initial volume (V1) = 780 mL = 780 cm³ Initial number of moles (n1) = 1.3 mol
We need to find the final volume (V2) when 0.21 mol is deducted, so: Final number of moles (n2) = n1 - 0.21 mol = 1.3 mol - 0.21 mol = 1.09 mol
Now we can solve for V2: V1/n1 = V2/n2 780 cm³ / 1.3 mol = V2 / 1.09 mol
Cross-multiplying the equation: 780 cm³ * 1.09 mol = V2 * 1.3 mol
Rearranging to solve for V2: V2 = (780 cm³ * 1.09 mol) / 1.3 mol
Calculating the final volume: V2 = 654 cm³
Therefore, the final volume of the container after deducting 0.21 mol of nitrogen at constant pressure and temperature is 654 cm³.