What is the fundamental difference between $K_c$ and $K_p$?

$K_c$ is defined by the molar concentrations of reactants and products in $mol \, dm^{-3}$, whereas $K_p$ is defined by the partial pressures of gaseous reactants and products. $K_p$ is specifically used for gas-phase equilibria.

Why are solids and pure liquids excluded from $K_p$ expressions?

The 'effective concentration' or vapor pressure of a solid or pure liquid is constant regardless of how much of the substance is present. Because these values do not change during the reaction, they are mathematically incorporated into the equilibrium constant itself.

When should you use square brackets $[ \, ]$ in a $K_p$ expression?

Never. Square brackets are the standard notation for molar concentration ($mol \, dm^{-3}$). Using them in a $K_p$ expression is a notation error; you should use $p(gas)$ or $(p_{gas})$ instead.

How does a change in total pressure affect the numerical value of $K_p$?

A change in total pressure does not affect the numerical value of $K_p$, provided the temperature remains constant. While the position of equilibrium may shift to maintain the ratio, the constant itself remains unchanged.

What is the formula for the partial pressure of a gas in a mixture?

Partial pressure is calculated by multiplying the mole fraction of the gas by the total pressure of the system ($p_A = X_A \cdot P_{total}$). This represents the contribution of that specific gas to the total pressure.

What happens to the units of $K_p$ if the number of moles of gaseous products equals the number of moles of gaseous reactants?

In this scenario, the units in the numerator and denominator will cancel out completely, resulting in a unitless $K_p$ value. This occurs because the sum of the powers in the numerator equals the sum of the powers in the denominator.

What is a common error when dealing with a reaction like $C(s) + CO_2(g) \rightleftharpoons 2CO(g)$?

A common error is including the solid carbon ($C(s)$) in the denominator of the $K_p$ expression. The correct expression is $K_p = \frac{p(CO)^2}{p(CO_2)}$, omitting the solid entirely.

How do you determine the power to which a partial pressure is raised in the $K_p$ expression?

The power is determined by the stoichiometric coefficient of that substance in the balanced chemical equation. For example, if the equation shows $3H_2(g)$, the partial pressure $p(H_2)$ is raised to the power of 3.

If a reaction is endothermic, how does increasing the temperature affect $K_p$?

For an endothermic reaction, increasing the temperature shifts the equilibrium to the right (favoring products). This increases the numerator of the $K_p$ expression, thereby increasing the numerical value of $K_p$.

Why might a student calculate the wrong units for $K_p$ even if their expression is correct?

This usually happens if the student fails to account for the powers in the expression when canceling units. For example, if the expression is $\frac{p^2}{p}$, the units should be $kPa^2 / kPa = kPa$, but a student might forget to square the unit in the numerator.

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5. Advanced Physical Chemistry

Deducing Kp Expressions

Summary

The equilibrium constant $K_p$ is a quantitative measure of the position of equilibrium for reversible reactions involving gases, expressed using partial pressures rather than concentrations. It provides a standardized way to predict the extent of a gaseous reaction at a specific temperature, where the expression is derived directly from the stoichiometric coefficients of the balanced chemical equation.

1. Definition & Core Concepts

A diagram showing the structure of a Kp expression with products over reactants and coefficients becoming exponents.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

Confusing Total Pressure with Partial Pressure: Students often mistakenly use the total system pressure in place of individual partial pressures. Partial pressure must be calculated first (usually via mole fraction) before being placed into the $K_p$ formula.
Incorrect Power Application: Forgetting to square or cube the partial pressure when the stoichiometric coefficient is 2 or 3 is a frequent calculation error.
Including Liquids: In reactions involving steam ( $H_2O(g)$ ), it is included. If the reaction involves liquid water ( $H_2O(l)$ ), it must be excluded. Always check the state symbol carefully.

Deducing Kp Expressions

Summary

1. Definition & Core Concepts

$K_p$ is the equilibrium constant for a reaction involving gases, where the 'p' denotes that the expression is formulated using the partial pressures of the reactants and products. Unlike $K_c$ , which uses molar concentrations, $K_p$ is specifically designed for gas-phase systems because the pressure of a gas is directly proportional to its concentration at a constant temperature.

The partial pressure of an individual gas in a mixture is the pressure that gas would exert if it occupied the entire volume alone. The sum of all partial pressures in a system equals the total pressure, a principle known as Dalton's Law of Partial Pressures.

In a $K_p$ expression, the partial pressure of a substance is denoted by a lowercase ' $p$ ' followed by the chemical formula in subscript or parentheses, such as $p(H_2)$ or $p_{H_2}$ .

A diagram showing the structure of a Kp expression with products over reactants and coefficients becoming exponents.

2. Underlying Principles

The $K_p$ expression is derived from the Law of Mass Action, which states that the rate of a chemical reaction is proportional to the product of the activities of the reactants. For gases, partial pressure serves as an accurate proxy for activity under ideal conditions.

For a general reversible reaction $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$ , the equilibrium constant is defined as: $K_p = \frac{p(C)^c \cdot p(D)^d}{p(A)^a \cdot p(B)^b}$

The value of $K_p$ is temperature-dependent. If the temperature remains constant, the value of $K_p$ remains constant regardless of changes in total pressure or the addition of reactants/products, as the system will shift its position to restore the ratio.