The equilibrium constant (Kc) for the gas phase reaction 2 NH3 N2 + 3 H2 is 3.0 x 10-3 at some temperature. The reaction is started by placing a 0.040-mol sample of ammonia in an empty one-liter flask. When equilibrium is established how much N2 is present?

1. ) 0.019 mol
2. ) 0.013 mol
3. ) 0.010 mol
4. ) 0.016 mol

I don't get the answer i have tried it over at least 10 times. I did the ice table and everything.

To find the amount of N2 present at equilibrium, we need to use the equilibrium constant (Kc) and the initial quantity of NH3. The balanced equation for the reaction is:

2 NH3 -> N2 + 3 H2

From the equation, we can see that for every 2 moles of NH3, we obtain 1 mole of N2. Therefore, the mole ratio of NH3 to N2 is 2:1.

The equilibrium constant (Kc) is given as 3.0 x 10^-3. This means that the ratio of the concentrations of the products to the reactants at equilibrium is 3.0 x 10^-3.

Let x be the amount of NH3 that reacts to form N2 at equilibrium. Since the mole ratio of NH3 to N2 is 2:1, the amount of N2 produced is also x (in moles).

At the start of the reaction, we have 0.040 moles of NH3. Therefore, at equilibrium, the amount of NH3 remaining is 0.040 - x moles.

Using the equilibrium constant expression:

Kc = [N2] / [NH3]^2

Substituting the equilibrium concentrations, we have:

3.0 x 10^-3 = x / (0.040 - x)^2

Simplifying the equation, we get:

3.0 x 10^-3 = x / (0.0016 - 0.080x + x^2)

Rearranging the equation, we have:

0 = x^2 - (0.0016 - 0.080x) / 3.0 x 10^-3

Multiplying through by 3.0 x 10^-3, we get:

0 = 3 x 10^3 x^2 - 0.53 + 26.6x

Next, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 3 x 10^3, b = 26.6, and c = -0.53.

Plugging in the values into the quadratic formula, we find two possible values for x. However, we need to discard the negative value since we cannot have negative amounts of N2.

Thus, the only acceptable value for x is approximately 0.013 mol.

Therefore, the answer is 0.013 mol (Option 2) of N2 is present at equilibrium.

A major suggestion: You MUST write an arrow; otherwise, we don't know where the reactants end and the products begin.

a. Place the arrow.
b. Set up an ICE chart.
c. Plug the ICE numbers into the Kc experession.
d. solve.

0.019mol