Calculating equilibrium partial pressures involves understanding how the initial partial pressures of reactants change as a reaction reaches equilibrium. The core concept is to track changes in partial pressures using a variable, often "x," based on the stoichiometry of the balanced chemical equation.
Understanding Equilibrium Partial Pressure
Equilibrium partial pressure refers to the partial pressure of a gas in a system when the rate of forward reaction equals the rate of the reverse reaction. At this point, there's no net change in concentrations of reactants and products. To calculate these, we need to use initial partial pressures and the change due to reaction, which is related by the variable "x".
General Forms and Their Impact on Partial Pressure Calculation
The change in partial pressure of reactants and products is directly linked to the reaction's stoichiometry. Consider the following two general reaction forms:
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Reactant(s) ⇌ Product(s): For reactions of this type, the equilibrium partial pressure of a reactant is its initial partial pressure minus x, and the equilibrium partial pressure of a product is x.
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Reactant(s) ⇌ 2 Product(s): For reactions where a single reactant is converted into two product molecules, the partial pressure change will be different. The equilibrium partial pressure of the reactant is still initial partial pressure minus x, while the partial pressure of the product is 2x.
How to Calculate Equilibrium Partial Pressures: Step-by-Step
Here's a breakdown of how to calculate equilibrium partial pressures:
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Identify Initial Partial Pressures: Note the initial partial pressures of all gaseous reactants and products.
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Set up an ICE Table (or equivalent): Create a table (or system of equations) with initial partial pressures, change in pressures (using “x”), and equilibrium pressures.
- I (Initial): List the initial partial pressures.
- C (Change): Use "x" to represent changes in partial pressures, considering the stoichiometry. Reactants will generally be (-x) and products (+x).
- E (Equilibrium): Calculate the equilibrium partial pressures based on initial values and changes (+x or -x)
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Define Equilibrium Partial Pressures:
- Reactants: Equilibrium Partial Pressure = Initial Partial Pressure - x
- Products:
- For reactions like Reactant(s) ⇌ Product(s): Equilibrium Partial Pressure = x
- For reactions like Reactant(s) ⇌ 2 Product(s): Equilibrium Partial Pressure = 2x
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Use the Equilibrium Constant (Kp): Once the expressions for the equilibrium partial pressures are known, use the equilibrium constant (Kp) expression and the values of Kp to solve for x. This may involve solving a quadratic equation.
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Calculate Equilibrium Partial Pressures: Once x is determined, substitute it back into the expressions derived in step 3 to find the equilibrium partial pressures of each reactant and product.
Example
Let’s consider a simple example:
If we have initial partial pressures of P(N2) = 2 atm and P(H2) = 3 atm, and initially no ammonia (P(NH3) = 0 atm):
| N2 (g) | 3H2(g) | 2NH3(g) | |
|---|---|---|---|
| Initial (I) | 2 | 3 | 0 |
| Change (C) | -x | -3x | +2x |
| Equilibrium (E) | 2 - x | 3 - 3x | 2x |
- The equilibrium partial pressure of N2 is (2-x) atm.
- The equilibrium partial pressure of H2 is (3-3x) atm.
- The equilibrium partial pressure of NH3 is (2x) atm.
Once you know the Kp for the reaction at a given temperature, you can substitute these values into the equilibrium constant expression and solve for x. Then, use x to calculate the actual partial pressures at equilibrium.
Key Considerations
- The value of x will differ depending on the initial conditions and the equilibrium constant.
- When dealing with more complex reactions, the coefficients in the balanced chemical equation dictate the multiples of "x" used.
- Equilibrium partial pressures are temperature-dependent; the equilibrium constant Kp changes with temperature.
By using this structured approach, you can accurately calculate equilibrium partial pressures for various gas-phase reactions.
