The equilibrium constant Kc for the reaction N21g2 + 3 H21g2 ∆ 2 NH31g2 is 4.20 at 600 K. When a quantity of gaseous NH3 was placed in a 1.00-L reaction vessel at 600 K and the reaction was allowed to reach equilibrium, the vessel was found to contain 0.200 mol of N2. How many moles of NH3 were placed in the vessel?

Video transcript

Hello. In this problem we are told that 500 Kelvin. The equilibrium constant for the foreign reaction is 1.68. If the reaction is performed in a one liter vessel at 500 Kelvin, how much nitrogen tetroxide must be placed in the vessel to contain .17 moles of nitrogen at equilibrium. Let's begin by writing an ice table. So we have our reaction, we have initial change and equilibrium. So we're asked how much nitrogen tetroxide do we have? So we'll call that initial amount A which you're trying to find. We'll assume we initially have no nitrogen or oxygen. Then the change. So our product is going to be converted back into react ints. So that means we're going to be producing our reactant. So this would be plus X. And plus two X. And then minus X. For the product. The equilibrium. Then we're combining the initial and the change. So this would be X two X and a minus X. So we're told that at equilibrium then the amount of nitrogen will be equal to 0.178. Are equal amount is X. For nitrogen. So that will be equal to 0.178. R. Two X. Then which will be the oxygen will be equal to two times that. So two times 20.178. Which will be equal to 0.356. So we can plug this information into our equilibrium constant expression. So equilibrium constant. Then it's equal to our product concentrations. That's the one power. Because the coefficient is one divided by the reactant concentrations. The nitrogen to the one power oxygen squared. And so we plug in the information from our ice table. So we have a minus X. Over and then the nitrogen is 0.178, and oxygen is 0.356. And we square that And we're told that the equilibrium constant is equal to 1.68. So this all equals 1.68. So we have a minus X, then is equal to 1.68 times 0.178 times 0.356 squared. And this all works out to 0.037899. And we do know what X is. So A. Then is equal to 0.37899 plus X. Which is 0.1780 point 037899 plus 0.178. So A then which is our initial concentration of di nitrogen. Tetroxide Is equal to 0.216 Moller. Thanks for watching. Hope this helps