RevisionDojo

Equilibrium Calculations in Chemistry

As discussed previously, the equilibrium constant ($ K $) provides a numerical measure of the balance between reactants and products at equilibrium.
For a general reaction: $$
aA + bB \rightleftharpoons cC + dD
$$
The equilibrium constant expression is: $$
K = \frac{[C]^c [D]^d}{[A]^a [B]^b}
$$ Here:
1. $ [... ] $ represents molar concentrations.
2. The exponents correspond to the stoichiometric coefficients in the balanced equation.

Example

For the reaction $ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $, the equilibrium constant expression is:$$
K = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}
$$

Step-by-Step: Calculating Equilibrium Concentrations

To calculate equilibrium concentrations, follow these steps:

Write the $ K $ Expression:
1. Start by writing the equilibrium constant expression for the reaction.
Define Initial and Equilibrium Concentrations:
1. Use an ICE (Initial, Change, Equilibrium) table to organize the data.
2. Define the initial concentrations, the changes during the reaction, and the equilibrium concentrations.
Substitute into the $ K $ Expression:
1. Substitute the equilibrium concentrations into the $ K $ expression, often in terms of $ x $, the change in concentration.
Solve for $ x $:
1. Solve the resulting equation to find $ x $, representing the change in concentration.
Calculate Equilibrium Concentrations:
1. Use $ x $ to calculate the equilibrium concentrations of all species.

Example question

Calculate the equilibrium concentrations for the reaction $ H_2(g) + I_2(g) \rightleftharpoons 2HI(g) $, where $ K = 50.0 $ and the initial concentrations are:

$[H_2] = 0.100 \, \text{mol dm}^{-3}$,
$[I_2] = 0.100 \, \text{mol dm}^{-3}$,
$[HI] = 0 \, \text{mol dm}^{-3}$.

Solution

Write the $ K $ expression:$$
K = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]}
$$
Define the changes using an ICE table:

Species	Initial ($\text{mol dm}^{-3}$)	Change ($\text{mol dm}^{-3}$)	Equilibrium ($\text{mol dm}^{-3}$)
$H_2$	0.100	$-x$	$0.100-x$
$I_2$	0.100	$-x$	$0.100-x$
$HI$	0	$+2x$	$2x$

Substitute into the $ K $ expression:$$
50.0 = \frac{(2x)^2}{(0.100 - x)(0.100 - x)}
$$
To solve for $ x $, expand and simplify:$$
50.0 = \frac{4x^2}{(0.100 - x)^2}
$$ $$
x = 0.078 \, \text{mol dm}^{-3}
$$
Calculate equilibrium concentrations:
$$[H_2] = [I_2] = 0.100 - 0.078 = 0.022 \, \text{mol dm}^{-3}$$ $$[HI] = 2x = 2(0.078) = 0.156 \, \text{mol dm}^{-3}$$

Tip

Always double-check your calculations and ensure units are consistent throughout the problem.

Approximation for Small $ K $

When $ K $ is very small (e.g., $ K< 10^{-3} $), the reaction heavily favors the reactants.
In such cases, the change in reactant concentration ($ x $) is often negligible compared to the initial concentration.
This allows for simplifications in calculations.

Steps for Approximation

Set Up the $ K $ Expression: Write the equilibrium constant expression as usual.
Assume Negligible Change: If $ K $ is small, assume $ [\text{Reactant}] - x \approx [\text{Reactant}] $.
Solve for $ x $: Substitute the approximation into the $ K $ expression and solve for $ x $.
Verify the Approximation:
1. Check whether $ x $ is less than 5% of the initial concentration.
2. If true, the approximation is valid.

Example question

For the reaction $ 2NO_2(g) \rightleftharpoons N_2O_4(g) $, $ K = 0.001 $ and the initial concentration of $ NO_2 $ is $ 0.100 \, \text{mol dm}^{-3} $. Calculate the equilibrium concentrations.

Solution

Write the $ K $ expression: $$
K = \frac{[N_2O_4]}{[NO_2]^2}
$$
Define equilibrium concentrations: $$[NO_2] = 0.100 - 2x$$ $$[N_2O_4] = x$$
Substitute into the $ K $ expression:$$
0.001 = \frac{x}{(0.100)^2}
$$
Solve for $ x $:$$
x = 0.001 \times 0.100^2 = 0.00001 \, \text{mol dm}^{-3}
$$
Verify the approximation:
- $ 2x = 0.00002 \, \text{mol dm}^{-3} $,
- $ 0.00002 \ll 0.100 $, so the approximation is valid.
Calculate equilibrium concentrations: $$[NO_2] \approx 0.100 \, \text{mol dm}^{-3}$$ $$[N_2O_4] = x = 0.00001 \, \text{mol dm}^{-3}$$

Unlock the rest of this chapter with a Free account

Nice try, unfortunately this paywall isn't as easy to bypass as you think. Want to help devleop the site? Join the team at https://revisiondojo.com/join-us. exercitation voluptate cillum ullamco excepteur sint officia do tempor Lorem irure minim Lorem elit id voluptate reprehenderit voluptate laboris in nostrud qui non Lorem nostrud laborum culpa sit occaecat reprehenderit

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Duis aute irure dolor in reprehenderit

Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit.

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Introduction to Equilibrium Calculations

Chemical equilibrium calculations allow us to predict the concentrations of reactants and products when a reaction reaches equilibrium.
This is crucial in industrial processes where maximizing product yield is essential.

AnalogyThink of equilibrium calculations like a recipe - if you know the exact proportions of ingredients (reactants), you can predict how much cake (product) you'll get.

ExampleIn the Haber process for ammonia production, knowing the equilibrium concentrations helps optimize conditions for maximum ammonia yield.

DefinitionEquilibrium ConcentrationThe concentration of reactants and products when a reversible reaction reaches a state where the forward and reverse reaction rates are equal.

DefinitionEquilibrium PositionThe relative concentrations of reactants and products at equilibrium, which can be shifted by changing conditions.

R2.3.6 Quantifying equilibrium concentrations (Higher Level Only) Notes

Equilibrium Calculations in Chemistry

Step-by-Step: Calculating Equilibrium Concentrations

Approximation for Small $ K $

Steps for Approximation

Unlock the rest of this chapter with a Free account

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Want a cheatsheet?

Unlock the rest of this chapter with a Free account

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Introduction to Equilibrium Calculations

Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

R2.3.6 Quantifying equilibrium concentrations (Higher Level Only) Notes

Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

Equilibrium Calculations in Chemistry

Step-by-Step: Calculating Equilibrium Concentrations

Approximation for Small $ K $

Steps for Approximation

Unlock the rest of this chapter with a Free account

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Want a cheatsheet?

Unlock the rest of this chapter with a Free account

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Introduction to Equilibrium Calculations