Without detailed equilibrium calculations, estimate the equilibrium concentration of SO3 when a mixture of 0.134 mol of SO2 and 0.067 mol of O2 in a 275 mL flask at 300oC combine to form SO3.

2 SO2(g) + O2(g) = 2 SO3(g)

Kc = 6.3x10^9

I tried doing an ICE chart, and also tried working through an equilibrium expression to solve for the concentration of SO3, but both methods got me wrong answers

It's hard to know exactly what is meant by "without 'detailed' calculations" estimate... We don't know how detailed the author wants it nor do we know what is considered an estimate.

I think the idea here is that with such a large Kc the equilibrium is far to the right which means that for all practical purposes all of the SO2 an O2 react to form 0.134 mol SO3. The concn then will be about 0.134/0.275L = about 0.487 or about 0.5M

At 627ºC, sulfur dioxide and oxygen gases combine to form sulfur trioxide gas. At equilibrium, the concentrations for sulfur dioxide, oxygen, and sulfur trioxide gases are .0060M, .0054M, and .0032M, respectively.

a. Write a balanced equation for the formation of one mole of sulfur trioxide.
b. Calculate K for the reaction @ 627ºC. (Note that gases need to be in atm.)

To estimate the equilibrium concentration of SO3 without performing detailed equilibrium calculations, we can make a simplifying assumption called the "initial assumption."

1. Start by writing the balanced chemical equation for the reaction:
2 SO2(g) + O2(g) → 2 SO3(g)

2. Determine the initial moles of each compound:
- SO2: 0.134 mol
- O2: 0.067 mol
- SO3: unknown (let's call it x)

3. Calculate the total moles of the reactants (SO2 and O2):
Total moles of reactants = 0.134 mol + 0.067 mol = 0.201 mol

4. Since we have a 275 mL flask, convert this volume into liters:
Volume = 275 mL = 275/1000 L = 0.275 L

5. Calculate the initial concentration of each reactant in moles per liter:
Concentration (M) = moles/volume = moles/0.275 L
- [SO2] = 0.134 mol/0.275 L
- [O2] = 0.067 mol/0.275 L

6. We can assume that the reaction goes to completion, meaning that all of the reactants (SO2 and O2) are converted to products (SO3) without any reactants remaining. Therefore, the concentration of SO3 at equilibrium will equal the total moles of reactants.

7. Set up an expression for the equilibrium constant (Kc):
Kc = [SO3]^2 / ([SO2]^2 * [O2])
Given Kc = 6.3x10^9

8. Using the initial concentrations and the equilibrium expression, we can set up an equation that approximates the equilibrium concentration of SO3:
(x)^2 / ([0.134/0.275]^2 * [0.067/0.275]) ≈ 6.3x10^9

9. Solve for x to get the equilibrium concentration of SO3.

Note: The initial assumption method provides an approximation and assumes full conversion of reactants to products. For precise calculations, you would need to solve the equilibrium expression with an ICE (Initial, Change, Equilibrium) table or use other iterative methods.