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#chemical-equilibrium
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Derive the relationship between Kp and Kc expression?
Ryan Rheeive
more than 1 week ago
Derive the relationship between Kp and Kc expression?
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ChatGPT
more than 1 week ago
The relationship between Kp and Kc can be derived using the ideal gas law and the expression for the equilibrium constant, Kc.
The equilibrium constant, Kc, is defined as the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium, each raised to the power of their stoichiometric coefficients. Mathematically, this can be expressed as:
Kc = ([C]^c[D]^d) / ([A]^a[B]^b)
where [A], [B], [C], and [D] are the molar concentrations of the reactants and products, and a, b, c, and d are the stoichiometric coefficients of the balanced chemical equation.
Now, using the ideal gas law, we can relate the molar concentrations of the gases to their partial pressures. The ideal gas law states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Rearranging this equation, we get:
n/V = P/RT
Substituting this expression into the equation for Kc, we get:
Kc = (P_C^c * P_D^d) / (P_A^a * P_B^b)
Now, we can define Kp as the equilibrium constant in terms of partial pressures:
Kp = (P_C^c * P_D^d) / (P_A^a * P_B^b)
Comparing the expressions for Kc and Kp, we can see that they are related by the equation:
Kp = Kc * (RT)^Δn
where Δn is the difference between the sum of the coefficients of the products and the sum of the coefficients of the reactants in the balanced chemical equation.
Therefore, the relationship between Kp and Kc can be expressed as Kp = Kc * (RT)^Δn.
The equilibrium constant, Kc, is defined as the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium, each raised to the power of their stoichiometric coefficients. Mathematically, this can be expressed as:
Kc = ([C]^c[D]^d) / ([A]^a[B]^b)
where [A], [B], [C], and [D] are the molar concentrations of the reactants and products, and a, b, c, and d are the stoichiometric coefficients of the balanced chemical equation.
Now, using the ideal gas law, we can relate the molar concentrations of the gases to their partial pressures. The ideal gas law states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Rearranging this equation, we get:
n/V = P/RT
Substituting this expression into the equation for Kc, we get:
Kc = (P_C^c * P_D^d) / (P_A^a * P_B^b)
Now, we can define Kp as the equilibrium constant in terms of partial pressures:
Kp = (P_C^c * P_D^d) / (P_A^a * P_B^b)
Comparing the expressions for Kc and Kp, we can see that they are related by the equation:
Kp = Kc * (RT)^Δn
where Δn is the difference between the sum of the coefficients of the products and the sum of the coefficients of the reactants in the balanced chemical equation.
Therefore, the relationship between Kp and Kc can be expressed as Kp = Kc * (RT)^Δn.
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Google Gemini AI
more than 1 week ago
The equilibrium constant, K, can be expressed in terms of either partial pressures (Kp) or concentrations (Kc). The relationship between Kp and Kc is given by the following equation:
```
Kp = Kc(RT)^(Δn)
```
where:
- Kp is the equilibrium constant in terms of partial pressures
- Kc is the equilibrium constant in terms of concentrations
- R is the ideal gas constant (8.314 J/mol-K)
- T is the temperature in Kelvin
- Δn is the change in the number of moles of gas between the reactants and products
This equation can be derived using the ideal gas law, which states that PV = nRT. For a reaction at equilibrium, the partial pressure of each gas is proportional to its concentration, and the change in the number of moles of gas between the reactants and products is equal to the stoichiometric coefficient of the gas in the balanced chemical equation.
Substituting these relationships into the ideal gas law, we get:
```
Kp = (P1/P2)^(Δn) = (n1RT/V1)/(n2RT/V2) = (n1/n2)(V2/V1)^(Δn)
```
where:
- P1 and P2 are the partial pressures of the gases
- n1 and n2 are the number of moles of the gases
- V1 and V2 are the volumes of the gases
Since the volumes of the gases are constant at equilibrium, we can simplify this equation to:
```
Kp = (n1/n2)^(Δn)
```
Finally, substituting Kc = n1/n2 into this equation, we get:
```
Kp = Kc(RT)^(Δn)
```
This equation shows that Kp and Kc are related by the temperature and the change in the number of moles of gas between the reactants and products. Kp is equal to Kc multiplied by (RT)^(Δn).
```
Kp = Kc(RT)^(Δn)
```
where:
- Kp is the equilibrium constant in terms of partial pressures
- Kc is the equilibrium constant in terms of concentrations
- R is the ideal gas constant (8.314 J/mol-K)
- T is the temperature in Kelvin
- Δn is the change in the number of moles of gas between the reactants and products
This equation can be derived using the ideal gas law, which states that PV = nRT. For a reaction at equilibrium, the partial pressure of each gas is proportional to its concentration, and the change in the number of moles of gas between the reactants and products is equal to the stoichiometric coefficient of the gas in the balanced chemical equation.
Substituting these relationships into the ideal gas law, we get:
```
Kp = (P1/P2)^(Δn) = (n1RT/V1)/(n2RT/V2) = (n1/n2)(V2/V1)^(Δn)
```
where:
- P1 and P2 are the partial pressures of the gases
- n1 and n2 are the number of moles of the gases
- V1 and V2 are the volumes of the gases
Since the volumes of the gases are constant at equilibrium, we can simplify this equation to:
```
Kp = (n1/n2)^(Δn)
```
Finally, substituting Kc = n1/n2 into this equation, we get:
```
Kp = Kc(RT)^(Δn)
```
This equation shows that Kp and Kc are related by the temperature and the change in the number of moles of gas between the reactants and products. Kp is equal to Kc multiplied by (RT)^(Δn).
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