Kp and Kc - Online Tutor, Practice Problems & Exam Prep

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

Your equilibrium constant is represented by the variable capital K. Now recall that the equilibrium constant, which can also be represented as K_EQ, can be expressed as K_P or K_C. Now K_P, we use this version of our equilibrium constant when dealing with gases in units of atmospheres. K_C will use this when dealing with aqueous solutions, which are typically found in molarity. Remember, molarity itself is moles per liter.

We're going to say here that K_P and K_C can be related together through the use of a formula. Now this formula is KP=KCRT^ΔN. Now K_C and K_P again are just equilibrium constants. They're just equilibrium constant based on the units that we're using, whether that's in atmospheres or molarity. R is our gas constant. If you've seen my videos on the ideal gas law, you know that R here equals 0.08206 liters times atmospheres over moles times K, and then temperature is T in Kelvin.

Now here, what is ΔN exactly? Well, ΔN, here's when we're looking at the moles of gases within our balanced chemical equation and here and it's just the gas coefficients of those gaseous compounds. Here ΔN equals the moles of gas as products minus the moles of gas as reactants. OK, so it's just products minus reactants. We look at our balance equation. We see which compounds on both sides of our arrows are reversible. Arrows are gases. We do the number of moles of gases products minus the number of moles of gas as reactants. That'll give us our ΔN.

So just remember your equilibrium constant can be expressed as K_C and K_P in the equation that connects them together is KP=KCRT^ΔN.

Kp and Kc Example

Here in this example question, it says calculate K_P for the following reaction with K_C equal to 0.77 at 570 Kelvin. All right, so here we're given our equation AT₂A gases react with 1B solid to produce CD gas plus 3 E gas. All right. The equation that connects K_P to K_C, remember is

K P = K C ⁢ R T ∆N

Here we're told that K_C is 0.77. R is our gas constant, which is 0.08206. Temperature needs to be in Kelvin, which it's already given in Kelvin, so we plug that in. Now ∆N, ∆N is our moles of gases products. So how many moles of gas do we have as products? We have one. We have three more, so that's 4 minus. The moles of gas is reactants. This is a solid, so we're going to ignore it. Here's a gas. There's two. So ∆N here equals 2.

All right, so then what we're going to do here is we're going to say 77. When we multiply our R&T together, what's found inside is 46.7742. Remember that still being squared? Then we're going to say

46.7742 2 = 2187.825786

Take that number, multiply it by 0.77 gives us 1684.625855 as our answer, but we want to do it in terms of sig figs.

77 has two sig figs, 570 has two sig figs. So we're just going to round this up to

1.7 ⁢ 10 3

Here we have our answer to two significant figures, so this would be our final value for K_P.

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

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

Value of ∆n

So when comparing K_P to K_C, it's important to understand the value of ΔN. Here we're going to say the value of ΔN can determine if K_C is greater than, less than, or equal to K_P. Remember the equation is K_P equals K_CRT to the ΔN. ΔN represents the moles of gas as products minus the moles of gas as reactants.

We can solve it mathematically to see how K_P and K_C relate to one another if we know what ΔN is. Or we can just simply say if more moles of gas are being produced. So basically you start out with let's say 3 moles of gases reactants and you end up with four moles of gases reactants. Your number of moles of gas has increased. So if more moles of gas are produced, that would mean that ΔN would be equal to or greater than one. Then that would mean K_P is greater than K_C.

So here just remember if ΔN is greater than or equal to 1 then K_P is greater than K_C or K_C is less than K_P. If ΔN is less than 0 then K_C is greater than K_P and if it's equal to 0 then they're equal to one another. Now why is that? Well if we do K_P equals K_CRT to the ΔN and we make ΔN equal to 0. Remember, anything to the zero power equals one. So K_P equals K_C times one. Anything times one is equal to itself. So K_P equals K_C.

So again, we can mathematically figure out what ΔN is to see what the relationship between K_C and K_P is. And remember this relationship. Or you can just simply say that if you have a certain number of moles of gases, reactants and if you go to the product side, there's even more moles of gas product, that means that K_P is going to be larger than K_C. OK. So just you can use that type of logic in order to subvert the math and just look at the question itself in a qualitative matter.

Alright, so let's put to practice what we just learned in the following example and practice questions.

Kp and Kc Example

For the final reactions, identify whether KP is greater than, less than, or equal to KC. So we're going to take a look at it in a qualitative as well as a quantitative manner and see if we get the same answer. So let's just do it for the first one and the first one. We have 4 moles of ammonia gas reacting with three moles of oxygen gas to produce 2 moles of nitrogen gas plus six moles of water vapor.

Here, if we were to figure out what ΔN is, remember ΔN equals moles of gas as products minus moles of gas as reactants. Our moles of gases products is 2 and six. So that's 8, -, 4 and then three. That's seven O. Recall that if ΔN is equal to or greater than one, that KP would be greater than KC. So that's what this is telling me. KP is greater than KC. We could also say that we start out with 7 moles of gases on the reactant side and now we have 8 moles of gases as products. The number of moles has increased.

KP is connected to gases in units of atmospheres, all right. So since there's more gas, more moles of gas being produced than we originally had, then KP would be greater than KC. So again, you can solve A mathematically, we could think of it in a qualitative way. More moles of gas on product side means that KP is greater than KC. Less moles of gas on product side means that KP is less than KC.

All right. So if we take a look at the next one, we have two moles of gas, it's reactants in a total of 2 moles of gases products. So the moles are equal on both sides. There wasn't an increase or decrease, so KP would be equal to KC. If you were to solve this using ΔN, you'll get definite N equal to 0 which remains. Also KP is equal to KC.

And then finally what do we have for the last one? We have 4 moles of gas as reactants and we only have two moles of gases products. So what do you think the ants will be here? Did our number of moles increase, decrease or stay the same? So we went from 4 moles of gas to two moles of gas. So the number of moles of gas went down. So that means KP would be smaller, KP would be less than KC. So these would be the answers for parts AB and C for the following example question.

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)

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

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.