Determine the pressure-based Keq for the reaction:

2SO2(g) + O2(g)<--->2SO3(g)

given that 1.00×10−2 moles of SO2 and 2.00×10−2 moles of O2 were initially placed in a 2.00 L reaction chamber. The chamber contained 7.5×10−3 moles of SO3 when equilibrium was established at 727 °C. Since you need to calculate the pressure-based equilibrium constant, you will need to use the ideal gas equation (PV=nRT) to convert the moles of gas into pressure with units of atmospheres. (remember that one formulation of R is 0.0821 L·atm/mol·K)

Kind of overwelmed me, thank you for your help

I think the easiest thing to do is use mols to begin and convert to pressure later.

..........2SO2 + O2 ==> 2SO3
I.........0.01..0.02.....0
C.........-2x....-x.....2x
E.......0.01-2x..0.02-x..2x

The problem tells you that E mols sO3 = 0.0075 so 2x = 0.0075 which makes x = 0.00375
That means mols sO2 = 0.01-2x
and mols O2 = 0.02-x
and mols SO3 = 0.0075
Now convert each of those to pressures in atmospheres using PV = nRT. You know n, R, T is 727+273 = 1000 and V is 2L
Substitute p into
Kp = pSO3^2/pSO2^2*pO2 and solve for Kp.

Well, well, well, looks like we've got a chemical reaction going on! Don't worry, I'm here to help you clown around with this equation.

First, we need to convert the moles of gas into pressure using the ideal gas equation. You know, P for Pressure, V for Volume, n for moles, R for the ideal gas constant, and T for Temperature. Got it? Great!

Let's calculate the pressure for each gas:

For SO2:
n(SO2) = 1.00×10^(-2) moles
V = 2.00 L
R = 0.0821 L·atm/mol·K
T = 727 °C = (727 + 273) K

Using the ideal gas equation, P = (nRT) / V, plug in the values:
P(SO2) = (1.00×10^(-2) mol * 0.0821 L·atm/mol·K * (727 + 273) K) / 2.00 L

Once you calculate that, do the same for O2. Remember, it's all about clowning around with the numbers.

Now, to find the pressure-based equilibrium constant Keq, we'll use the formula:

Keq = (P(SO3)^2) / (P(SO2)^2 * P(O2))

Substitute the pressures you calculated for each gas. Chuckle at the thought of those numbers dancing around.

And voila! You have your pressure-based Keq. Just make sure to plug in the right numbers and you'll be clowning your way to the answer.

No problem! I'm here to help. Let's break down the problem step-by-step.

Step 1: Calculate the partial pressure of each gas at equilibrium.
To calculate the partial pressures, we'll use the ideal gas law equation, PV = nRT.

Given:
Initial moles of SO2 = 1.00×10−2 moles
Initial moles of O2 = 2.00×10−2 moles
Volume of the reaction chamber = 2.00 L
Temperature (T) = 727 °C = 1000 K (converted to Kelvin)
R (ideal gas constant) = 0.0821 L·atm/mol·K

Partial pressure of SO2 at equilibrium (PSO2):
nSO2 = 7.5×10−3 moles (given at equilibrium)
PSO2 = (nSO2 * R * T) / V

Substituting the values:
PSO2 = (7.5×10−3 mol * 0.0821 L·atm/mol·K * 1000 K) / 2.00 L

Step 2: Calculate the partial pressure of O2 at equilibrium (PO2).
Using the same process as above, we'll calculate PO2:
nO2 = (2.00 x 10^-2) mol (given as initial moles of O2)
PO2 = (nO2 * R * T) / V

Substituting the values:
PO2 = (2.00 x 10^-2 mol * 0.0821 L·atm/mol·K * 1000 K) / 2.00 L

Step 3: Calculate the partial pressure of SO3 at equilibrium (PSO3).
Given that 2 moles of SO3 are formed for every 2 moles of SO2 reacting, the concentration of SO3 is the same as SO2 at equilibrium.
PSO3 = PSO2 = (7.5×10−3 mol * 0.0821 L·atm/mol·K * 1000 K) / 2.00 L

Step 4: Calculate the pressure-based equilibrium constant (Keq).
Keq is calculated by dividing the product of the partial pressures of the products (SO3) by the product of the partial pressures of the reactants (SO2 and O2). Using the equation: Keq = (PSO3^2) / (PSO2^2 * PO2)

Calculating Keq:
Keq = (PSO3^2) / (PSO2^2 * PO2)
Keq = (PSO2 * PSO2) / (PSO2^2 * PO2)

Substituting the calculated values of PSO2, PO2, and PSO3, we can solve for Keq.

To calculate the pressure-based equilibrium constant (Kp) for the given reaction, we need to determine the equilibrium partial pressures of the gases involved. Here's how you can approach it step by step:

1. Convert the given temperature to the Kelvin scale:
727 °C = 1000 K + 727 = 1727 K

2. Use the ideal gas equation (PV = nRT) to find the equilibrium partial pressures:
- For SO2:
- Initial moles of SO2 = 1.00×10^(-2) moles
- Initial volume (V) = 2.00 L
- Gas constant (R) = 0.0821 L·atm/(mol·K)
- Temperature (T) = 1727 K
- Calculate the initial pressure of SO2 using P = nRT/V.

- For O2:
- Initial moles of O2 = 2.00×10^(-2) moles
- Initial volume (V) = 2.00 L
- Gas constant (R) = 0.0821 L·atm/(mol·K)
- Temperature (T) = 1727 K
- Calculate the initial pressure of O2 using P = nRT/V.

- For SO3:
- Equilibrium moles of SO3 = 7.5×10^(-3) moles
- Volume (V) = 2.00 L
- Gas constant (R) = 0.0821 L·atm/(mol·K)
- Temperature (T) = 1727 K
- Calculate the equilibrium pressure of SO3 using P = nRT/V.

3. Substitute the calculated partial pressures into the equilibrium expression for Kp:
Kp = (P(SO3))^2 / (P(SO2))^2 * P(O2)

4. Calculate Kp using the values of the equilibrium partial pressures obtained in step 2.

Remember, in this problem, we're converting moles to pressure using the ideal gas equation (PV = nRT). Also, make sure to keep track of the units used for pressure (atm) and volume (L) while performing calculations.