Kp and Kc: Videos & Practice Problems

Understanding the relationship between K_P and K_C, the equilibrium constants for gaseous systems and aqueous solutions, respectively, is essential in chemical equilibrium. K_P is used with gases measured in atmospheres, while K_C is used for concentrations in molarity (moles per liter). They are connected by the equation:

K_P=K_C(RT)(∆N) where R is the gas constant (0.08206 L·atm/mol·K), T is the temperature in Kelvin, and ΔN is the change in moles of gas (moles of gaseous products minus moles of gaseous reactants). The value of ΔN determines if K_P is greater than, less than, or equal to K_C. If ΔN is positive, K_P > K_C; if ΔN is negative, K_C > K_P; if ΔN is zero, K_P = K_C, since any number to the power of zero equals one. This relationship can be used to predict the direction of change in equilibrium conditions or to calculate one constant from the other when the conditions of a reaction are known.

Kp vs. Kc Formula

The equilibrium constant, denoted as \( K \) or \( K_{eq} \), is a crucial concept in chemical equilibrium, representing the ratio of the concentrations of products to reactants at equilibrium. It can be expressed in two forms: \( K_p \) and \( K_c \). The \( K_p \) is used when dealing with gases and is measured in units of atmospheres, while \( K_c \) is applicable to aqueous solutions, typically expressed in molarity (moles per liter).

To relate \( K_p \) and \( K_c \), the following equation is utilized:

\( K_p = K_c \cdot R \cdot T^{\Delta n} \)

In this equation, \( R \) represents the gas constant, which is \( 0.08206 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}) \), and \( T \) is the temperature measured in Kelvin. The term \( \Delta n \) is defined as the difference in the number of moles of gaseous products and reactants, calculated as:

\( \Delta n = n_{products} - n_{reactants} \)

Here, \( n \) refers to the coefficients of the gaseous compounds in the balanced chemical equation. By identifying the moles of gas on both sides of the equilibrium expression, one can determine \( \Delta n \) and thus connect \( K_p \) and \( K_c \) effectively.

In summary, understanding the relationship between \( K_p \) and \( K_c \) through the equation \( K_p = K_c \cdot R \cdot T^{\Delta n} \) is essential for analyzing chemical equilibria, particularly when transitioning between gaseous and aqueous systems.

Calculate Kp Example

To calculate the equilibrium constant \( K_p \) for the reaction given that \( K_c = 0.77 \) at a temperature of 570 K, we can use the relationship between \( K_p \) and \( K_c \), which is expressed by the formula:

\[ K_p = K_c \cdot R \cdot T^{\Delta n} \]

In this equation:

• \( R \) is the ideal gas constant, \( 0.08206 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \)
• \( T \) is the temperature in Kelvin, which is given as 570 K
• \( \Delta n \) is the change in the number of moles of gas, calculated as the moles of gaseous products minus the moles of gaseous reactants.

For the reaction:

2 A(g) + 1 B(s) ⇌ C(g) + 3 E(g)

We identify the moles of gas in the products: 1 (from C) + 3 (from E) = 4 moles. The moles of gas in the reactants consist only of A, which has 2 moles. Therefore:

\[ \Delta n = 4 - 2 = 2 \]

Now, substituting the known values into the equation:

\[ K_p = 0.77 \cdot 0.08206 \cdot 570^{2} \]

Calculating \( 570^{2} \):

\[ 570^{2} = 324900 \]

Next, we calculate \( 0.08206 \cdot 324900 \):

\[ 0.08206 \cdot 324900 \approx 26564.07494 \]

Now, multiplying this result by \( K_c \):

\[ K_p = 0.77 \cdot 26564.07494 \approx 20453.93 \]

Finally, rounding to the appropriate number of significant figures (2 significant figures, based on \( K_c \) and temperature), we express the final answer as:

\[ K_p \approx 2.0 \times 10^{4} \]

This value represents the equilibrium constant \( K_p \) for the reaction at the specified temperature.

Partial pressures of the following equilibrium mixture at 955 K are: 130 torr methane, 92 torr hydrogen sulfide, 167 torr hydrogen gas and 532 torr carbon disulfide. What is the value of Kc at 955 K?
CH4(g) + 2 H2S(g) ⇌ 4 H2(g) + CS2(g)

• A. 1.1×10–4
• B. 1.3×10–5
• C. 8.3×10–3
• D. 1.0×10–2

Answer: (A)

Consider the hypothetical reaction: ? X(g) + 3 Y(g) ⇌ 3 Z(g), where K_p = 1.16 x 10^–3 and K_c = 1.3 at 135°C. Find the value of the coefficient of X.

• A. 5
• B. 3
• C. 4
• D. 2

Answer: (D)

Kp vs Kc Relationship

When comparing the equilibrium constants \( K_p \) and \( K_c \), understanding the concept of \( \Delta n \) is crucial. The value of \( \Delta n \) is defined as the difference between the moles of gaseous products and the moles of gaseous reactants. Mathematically, this relationship is expressed in the equation:

\( K_p = K_c \cdot R^T^{\Delta n} \)

Here, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. The implications of \( \Delta n \) can help determine the relationship between \( K_p \) and \( K_c \). If \( \Delta n \) is greater than or equal to 1, it indicates that more moles of gas are produced in the reaction, leading to \( K_p \) being greater than \( K_c \). Conversely, if \( \Delta n \) is less than 0, \( K_c \) will be greater than \( K_p \). When \( \Delta n \) equals 0, both constants are equal, as any number raised to the power of 0 equals 1, resulting in:

\( K_p = K_c \cdot 1 \)

This means that \( K_p \) and \( K_c \) are equivalent under these conditions. To summarize, if the reaction produces more moles of gas, \( K_p \) will be larger than \( K_c \). If the reaction consumes gas, \( K_c \) will be larger. This qualitative understanding can often simplify the analysis of equilibrium constants without extensive calculations.

To reinforce this concept, consider practicing with examples that require you to calculate \( \Delta n \) and determine the relationship between \( K_p \) and \( K_c \) based on the moles of gas involved in the reaction.

Kp vs Kc Relationship Example

In chemical reactions, the relationship between the equilibrium constants \( K_p \) and \( K_c \) can be determined by analyzing the change in the number of moles of gas during the reaction. This change is represented by \( \Delta n \), which is calculated as the moles of gaseous products minus the moles of gaseous reactants.

For the first reaction, where 4 moles of ammonia gas react with 3 moles of oxygen gas to produce 2 moles of nitrogen gas and 6 moles of water vapor, we can calculate \( \Delta n \) as follows:

\( \Delta n = \text{moles of products} - \text{moles of reactants} = (2 + 6) - (4 + 3) = 8 - 7 = 1 \)

Since \( \Delta n \) is greater than 0, it indicates that the number of moles of gas has increased, leading to the conclusion that \( K_p > K_c \). This is because an increase in the number of moles of gas on the product side favors the formation of products, which is reflected in the equilibrium constant.

In the second reaction, if we have 2 moles of gas as reactants and 2 moles of gas as products, the calculation for \( \Delta n \) is:

\( \Delta n = 2 - 2 = 0 \)

Here, since \( \Delta n \) equals 0, it follows that \( K_p = K_c \). This indicates that the number of moles of gas remains unchanged during the reaction.

For the final reaction, where 4 moles of gas as reactants yield 2 moles of gas as products, we calculate \( \Delta n \) as:

\( \Delta n = 2 - 4 = -2 \)

In this case, since \( \Delta n \) is less than 0, it shows that the number of moles of gas has decreased. Therefore, we conclude that \( K_p < K_c \). A decrease in the number of moles of gas on the product side suggests that the equilibrium favors the reactants.

In summary, the relationship between \( K_p \) and \( K_c \) can be qualitatively and quantitatively assessed through the change in moles of gas, providing a clear understanding of how equilibrium constants relate to the stoichiometry of the reaction.

For which reaction(s) will K_p = K_c?
a) N₂(g) + O₂(g) ⇌ 2 NO(g)
b) CaCO₃(s) ⇌ CaO(s) + CO₂(g)
c) 2 CH₄(g) ⇌ C₂H₂(g) + 3 H₂(g)
d) H₂O(g) + CO(g) ⇌ H₂(g) + CO₂(g)

• A. a) only
• B. b) only
• C. c) only
• D. d) only
• E. a) and d)
• F. b) and c)

Answer: (E)

Select the correct choice below for the reaction:  PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

• A. K_p = K_c
• B. K_p > K_c
• C. K_p < K_c
• D. K_eq = K_p
• E. None of the following

Answer: (B)

Here’s what students ask on this topic:

How can I find Kp from Kc?

To find the equilibrium constant for gases in terms of partial pressures (K_p) from the equilibrium constant for concentrations (K_c), you need to use the relationship between them, which involves the ideal gas law. The formula to convert K_c to K_p is:

K_p = K_c (RT)^Δn

where:

• K_p is the equilibrium constant in terms of partial pressure.
• K_c is the equilibrium constant in terms of concentration.
• R is the ideal gas constant (0.0821 L*atm/mol*K).
• T is the temperature in Kelvin.
• Δn is the change in moles of gas, calculated by subtracting the sum of the moles of gaseous products from the sum of the moles of gaseous reactants in the balanced chemical equation.

Remember, this conversion is only necessary for reactions involving gases, and Δn is crucial as it accounts for the volume change in the reaction. If Δn is zero, K_p equals K_c, as the (RT)^Δn term would equal 1.

How can I find K_c from K_p?

To find the equilibrium constant in terms of concentration (K_c) from the equilibrium constant in terms of pressure (K_p), you need to use the relationship that connects them, which involves the change in the number of moles of gas in the reaction. The formula is:

$K_c=K_p\left(RT\right){-}^{\mathrm{\Delta n}}$

Where:

• K_c is the equilibrium constant in terms of concentration (mol/L)
• K_p is the equilibrium constant in terms of pressure (atm)
• R is the ideal gas constant (0.0821 L*atm/mol*K)
• T is the temperature in Kelvin (K)
• Δn is the change in moles of gas (moles of gaseous products - moles of gaseous reactants)

To use this formula, you need to know the temperature at which the reaction is taking place and the stoichiometry of the reaction to calculate Δn. Remember that Δn can be positive, negative, or zero, depending on the reaction. Once you have these values, you can plug them into the formula to calculate K_c from K_p.

Which reactions have K_p equal to K_c?

The relationship between K_p (the equilibrium constant in terms of partial pressures) and K_c (the equilibrium constant in terms of molar concentrations) depends on the change in the number of moles of gas during a reaction. K_p is equal to K_c when the number of moles of gaseous reactants is the same as the number of moles of gaseous products. This is because the change in the number of moles of gas (Δn) is zero, and thus, the factor that relates K_p to K_c, which involves the gas constant (R) and the temperature (T) raised to the power of Δn, does not affect the equilibrium constants.

Mathematically, this is expressed as:

$K_p=K_c\left(RT\right){\Delta }^n$

When Δn = 0, the term (RT)^Δn becomes 1, and therefore:

$K_p=K_c$

So, reactions in which the number of moles of gases on both sides of the chemical equation are the same have K_p equal to K_c

How can I calculate Kp without Kc?

To calculate the equilibrium constant for gases in terms of partial pressures (K_p) without having the equilibrium constant in terms of concentration (K_c), you need to use the relationship between K_p and K_c, which is derived from the ideal gas law. This relationship is given by the equation:

K_p = K_c (RT)^Δn

Where:

• K_p is the equilibrium constant for partial pressures.
• K_c is the equilibrium constant for concentrations.
• R is the ideal gas constant, which is 0.0821 L*atm/(mol*K).
• T is the temperature in Kelvin.
• Δn is the change in moles of gas, calculated as the difference between the moles of gaseous products and the moles of gaseous reactants.

If you do not have K_c, you need to find a way to determine it from other given data, such as equilibrium concentrations or partial pressures of the reactants and products. Once you have K_c, you can then use the above equation to find K_p. If you cannot determine K_c from given data, it is not possible to calculate K_p directly, as K_p and K_c are inherently related.