1. Write the balanced chemical equation and the equilibrium expression:
The balanced chemical equation for the reaction is:
```
SO3(g) + NO(g) ⇌ SO2(g) + NO2(g)
```
The equilibrium expression is:
```
Keq = ([SO2][NO2]) / ([SO3][NO])
```
2. Set up an ICE table:
| | SO3 | NO | SO2 | NO2 |
|-------|-------|-------|-------|-------|
| Initial| 1.7 M | 0 | 0.070 M | 1.3 M |
| Change | -x | -x | +x | +x |
| Equil | 1.7-x | -x | 0.070+x | 1.3+x |
3. Substitute the equilibrium concentrations into the equilibrium expression:
```
10.8 = ((0.070 + x)(1.3 + x)) / ((1.7 - x)(x))
```
4. Solve for x:
This equation is a quadratic equation. You can solve it using the quadratic formula or by simplifying the equation and making approximations.
* Approximation: Since Keq is relatively large, we can assume that the change in concentration (x) is small compared to the initial concentrations of SO3, SO2, and NO2. This allows us to simplify the equation:
```
10.8 ≈ (0.070 * 1.3) / (1.7 * x)
```
* Solving for x:
```
x ≈ (0.070 * 1.3) / (10.8 * 1.7) ≈ 0.0053 M
```
5. Calculate the equilibrium concentration of NO:
```
[NO] = -x ≈ -0.0053 M
```
Since the concentration cannot be negative, this indicates our approximation was not valid. We need to solve the full quadratic equation.
Solving the Quadratic Equation:
1. Expand the equation from step 3.
2. Rearrange it into a standard quadratic form (ax² + bx + c = 0).
3. Use the quadratic formula to solve for x.
Important: The quadratic formula will give you two solutions for x. You need to choose the solution that makes physical sense (i.e., a positive value for [NO]).
After solving the quadratic equation, you'll get the equilibrium concentration of NO.
