How many moles of N are in a flask with a volume of 983.16 mL at a pressure of 100.9 kPa and a temperature of 408.6 K?

To solve this problem, we can use the ideal gas law, which is PV = nRT.

Here's the step-by-step solution:

1. Convert the volume from mL to L because the ideal gas law requires the volume to be in liters. 1 L = 1000 mL, so 983.16 mL = 0.98316 L.

2. Convert the pressure from kPa to atm because the ideal gas law requires the pressure to be in atmospheres. 1 atm = 101.325 kPa, so 100.9 kPa = 100.9/101.325 = 0.9958 atm.

3. Plug the values into the ideal gas law (PV = nRT), where P is the pressure, V is the volume, n is the number of moles (which we're trying to find), R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin.

0.9958 atm * 0.98316 L = n * 0.0821 L·atm/K·mol * 408.6 K

4. Solve for n (the number of moles):

n = (0.9958 atm * 0.98316 L) / (0.0821 L·atm/K·mol * 408.6 K) = 0.0296 mol

So, there are approximately 0.0296 moles of N in the flask.