# Determining final concentrations of a Reaction given an equilibrium K

• BrettJimison
In summary, the conversation discusses the use of a Kc equation to calculate the final concentrations of SO2, O2, and SO3 in a chemical equilibrium reaction. The given Kc value for the forward reaction is flipped to calculate the inverse Kc for the reverse reaction. A "rice" table is then used to set up the Kc equation and solve for the unknown variable x. A possible error in rounding the calculated value of x is mentioned, but it is determined that the original cubic equation was correct.
BrettJimison

## Homework Statement

Rxn: 2SO2 (g) + O2 (g) $\Leftrightarrow$ 2SO3 (g)

If the initial concentration of SO3 is .500 M (moles/liter) @1500K, what are the final concentrations of [SO2], [O2] and [SO3]. Kc = .15

Stop when you get to the cubic equation

## Homework Equations

RICE table

Kc= [SO3]2/ [O2][SO2]2 This is equilibrium quotient for forward reaction. I will flip it to get reverse reaction Kc equation

## The Attempt at a Solution

This is the Kc given for the forward reaction. If I flip the reaction around I invert the Kc and it becomes = 6.6667 (for the reverse reaction)

I then used a "rice" table with the initial concentration of SO3 and "x" variable for the SO2 and O2[

Plugging these values in I get the kc equation:

6.6667= [2x]2[x]/[.500-2x]

I'm not getting the correct cubic equation when expanding this quotient. I'm sure of my math, so I was wondering if I'm setting up the quotient wrong? - Thanks!

You don't need to reverse the reaction (you flipped and calculated the inverse of the Kc, which effectively cancels out).

What is the "correct" answer you are expecting to get? At first sight I don't see anything wrong with your work.

Looks OK to me too. Maybe the problem is this is a fairly complete conversion so don't round down too much your x as this could introduce considerable error in your (0.5 - 2x) when you back calculate to check?

(I get x = 0.24566)

Thanks for the input Borek and epenguin.
If turns out there was an error on the answer sheet I was given.
My cubic equation was correct after all.

Your approach is correct. The equilibrium constant, Kc, is indeed equal to 6.6667 when the reaction is flipped to the reverse direction. However, the cubic equation that you are getting may not be correct due to a mistake in setting up the RICE table or a miscalculation in solving the equation. I would suggest double-checking your RICE table and making sure that your calculations for the equilibrium concentrations are correct. You can also try using an online equilibrium calculator to check your results. If you are still having trouble, please provide your full calculations so I can assist you further.

## 1. What is equilibrium K and why is it important in determining final concentrations of a reaction?

Equilibrium K, also known as the equilibrium constant, is a ratio of the concentrations of the products to the concentrations of the reactants at equilibrium in a chemical reaction. It is important because it helps determine the direction and extent of a reaction at equilibrium.

## 2. How is equilibrium K calculated?

Equilibrium K is calculated by dividing the concentration of the products by the concentration of the reactants, with each concentration raised to the power of its coefficient in the balanced chemical equation. The resulting value is a constant at a given temperature for a specific reaction.

## 3. Can equilibrium K be changed?

No, equilibrium K is a constant value for a specific reaction at a given temperature. However, the equilibrium K value can be affected by changing the temperature of the reaction.

## 4. How does the value of equilibrium K relate to the direction of a reaction?

If the equilibrium K value is greater than 1, it indicates that there are more products than reactants at equilibrium and the reaction proceeds in the forward direction. If the equilibrium K value is less than 1, it indicates that there are more reactants than products at equilibrium and the reaction proceeds in the reverse direction. If the equilibrium K value is equal to 1, it indicates that the concentrations of the products and reactants are equal at equilibrium and the reaction is at equilibrium.

## 5. How does the initial concentrations of reactants affect the final concentrations of products at equilibrium?

The initial concentrations of reactants do not directly affect the final concentrations of products at equilibrium. However, they do affect the time it takes for the reaction to reach equilibrium and the amount of products that will be present at equilibrium. The equilibrium K value remains constant regardless of the initial concentrations of reactants.

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