Phosphorus pentachloride decomposes according to the chemical equation:

PCl5(g)<--> PCl3(g)+Cl2(g)

Kc = 1.80 at 250 degrees Celsius

A 0.352 mol sample of PCl5(g) is injected into an empty 4.45 L reaction vessel held at 250 °C. Calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium.

PCl5 = ?
PCl3 = ?

do the ice table

species initial final
PCl5 .352/4.45 (.352/4.45-x)
PCl3 0 x
CL2 0 x
where numbers are in moles per liter

K=x^2/(.352/4.45-x)

you know k, solve for x, then the concentrations listed on your ICE table.

Thank you! What did you get as answers? My answers were not correct.

If you will post your work someone will be glad to find the error for you.

To calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium, we need to first set up an ICE table and then use the given equilibrium constant (Kc) to solve for the unknowns.

Step 1: Set up the ICE table:
PCl5(g) <--> PCl3(g) + Cl2(g)
Initial: 0.352 mol 0 mol 0 mol
Change: -x mol +x mol +x mol
Equilibrium: 0.352 - x x x

Step 2: Write down the expression for Kc:
Kc = [PCl3] * [Cl2] / [PCl5]

Since the initial concentrations of PCl3 and Cl2 are both zero, we can ignore them in the expression.

Kc = x * x / (0.352 - x)

Step 3: Use the given Kc value and the known equilibrium concentrations to solve for x.
Kc = 1.80
1.80 = x^2 / (0.352 - x)

Solving this equation will give us the value of x, which represents the equilibrium concentration of PCl3 (and also Cl2, since they have the same coefficient in the balanced equation).

Step 4: Solve the equation to find x:
1.80 = x^2 / (0.352 - x)

Rearrange the equation:
1.80 * (0.352 - x) = x^2
0.6336 - 1.80x + 1.80x = x^2
x^2 - 1.80x + 0.6336 = 0

Now you can solve this quadratic equation. Use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -1.80, and c = 0.6336. Plug in these values into the quadratic formula to solve for x.

Step 5: Calculate the equilibrium concentrations:
Use the value of x obtained from Step 4 to calculate the equilibrium concentrations of PCl5 and PCl3.

PCl5 = 0.352 - x
PCl3 = x

Evaluate these expressions using the value of x obtained in Step 4 to find the equilibrium concentrations of PCl5 and PCl3.