The decomposition reaction for PCl5 for which the equilibrium constant is 0.030. If you begin an experiment with 0.040M PCl5. What are the expected equilibrium concentrations of all species.

PCl5 ⇄ PCl3 + Cl2

0.030 = [PCl3] [Cl2] / [PCl5] = x * x / (0.040 - x)

x^2 + 0.030 x - 0.0012 = 0

solve for x

Thank you!

What would i pick if both of the roots will result into positive concentration of PCl5

To determine the expected equilibrium concentrations of all species in the decomposition reaction of PCl5, we can use the equilibrium constant and the stoichiometry of the reaction.

The balanced equation for the decomposition of PCl5 is:

PCl5 ⇌ PCl3 + Cl2

According to the given information, the equilibrium constant (K) for this reaction is 0.030.

Let's assume x represents the change in concentration (in moles per liter) for PCl5, PCl3, and Cl2 at equilibrium.

At the start of the reaction, the concentration of PCl5 is given as 0.040 M. Since the decomposition reaction only produces PCl3 and Cl2, the concentration of PCl3 and Cl2 at the start is 0 M.

At equilibrium, the concentration of PCl5 will decrease by x, and the concentrations of PCl3 and Cl2 will both increase by x.

Therefore, the equilibrium concentrations are:

PCl5: 0.040 - x M

PCl3: x M

Cl2: x M

To determine the value of x, we can use the equilibrium constant expression:

K = ([PCl3] * [Cl2]) / [PCl5]

Plugging in the equilibrium concentrations:

0.030 = (x * x) / (0.040 - x)

Now, solving this equation for x can be a bit more complex. One way to approach it is by rearranging the equation and using the quadratic formula:

0.030(0.040 - x) = x^2

0.0012 - 0.030x = x^2

x^2 + 0.03x - 0.0012 = 0

Using the quadratic formula:

x = (-0.03 ± √((-0.03)^2 - 4 * 1 * (-0.0012))) / (2 * 1)

Simplifying this equation will give two possible values for x. However, we need to choose the appropriate value based on the context of the problem.

Once you have determined the value of x, you can substitute it back into the expressions for the equilibrium concentrations to find the expected values for PCl5, PCl3, and Cl2 at equilibrium.