If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circ*mstances, the equilibrium concentration is approximately equal to its initial concentration. This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial concentrations. However, to make this assumption, the change in the concentration of a weak acid or base, i.e., x, must be less than 5% of its initial concentration. If x is more than 5%, then the quadratic formula needs to be used to solve the equilibrium equation.
Calculation of Equilibrium Concentrations Using an Algebra-Simplifying Assumption
What are the concentrations at equilibrium of a 0.15 M solution of HCN?
Using x to represent the concentration of each product at equilibrium gives this ICE table.
| HCN (aq) | H+ (aq) | CN− (aq) |
| Initial Concentration (M) | 0.15 | 0 | 0 |
| Change (M) | −x | +x | +x |
| Equilibrium Concentration (M) | 0.15 − x | x | x |
Substitute the equilibrium concentration terms into the Kc expression
rearrange to the quadratic form and solve for x
Thus, [H+] = [CN–] = x = 8.6 × 10–6 M and [HCN] = 0.15 – x = 0.15 M.
Note in this case that the change in concentration is significantly less than the initial concentration (a consequence of the small K), and so the initial concentration experiences a negligible change:
This approximation allows for a more expedient mathematical approach to the calculation that avoids the need to solve for the roots of a quadratic equation:
The value of x calculated is, indeed, much less than the initial concentration
and so the approximation was justified. If this simplified approach were to yield a value for x that did not justify the approximation, the calculation would need to be repeated without making the approximation.
This text has been adapted from Openstax, Chemistry 2e, Section 13.4 Equilibrium Calculations.
FAQs
You can use the "x-is-small" approximation when the equilibrium constant has a value of less than 10^-3. With this condition, you can assume that the concentration of the reactants stays the same throughout the reaction to equilibrium because a very small amount is being consumed to make products.
In which one of the following conditions is the small x assumption valid? ›
You can use the "x-is-small" approximation when the equilibrium constant has a value of less than 10^-3. With this condition, you can assume that the concentration of the reactants stays the same throughout the reaction to equilibrium because a very small amount is being consumed to make products.
When can x be ignored in an ice table? ›
To determine whether x is negligible, compare the magnitude of the last decimal place of the concentration of the acid to the magnitude of the equilibrium constant. If the difference in magnitude is greater than 100, the x may be neglected.
What is the assumption rule in chemistry? ›
We divide x by the initial concentration and multiply by 100. If the answer is less than 5%, the assumption is valid. If it is 5% or greater, the assumption is not valid and the quadratic formula must be used to calculate x.
What is the 5% rule in equilibrium? ›
The 5% approximation rule is a guideline used in chemistry to simplify calculations involving weak acids and bases. It states that if the ionization of a weak acid or base is less than 5%, then the concentration of the un-ionized species can be approximated as equal to the initial concentration.
What is the small X assumption? ›
The small x assumption is an approximation that can be used under certain conditions to simplify solving the equilibrium expression and to avoid using the quadratic formula.
What does "x is small" mean? ›
The "x-is-small" approximation is based on the idea that if the system can be arranged so it starts “close” to equilibrium, then if the change (x) is small compared to any initial concentrations, it can be neglected.
How to determine if x is small? ›
We must test x to ensure that the small x approximation was a good approximation. If x is within 5% of the number it was being subtracted from (or added to), the small x approximation is good enough. Note: The “5%” threshold is somewhat arbitrary.
Why can we ignore a small X in the first case but not in the second? ›
Explain why we can ignore a small x in the first case but not the second. When adding or subtracting a small value of x, we can often ignore x because of significant figures. In addition and subtraction, the number of significant figures depends on the number with the fewest decimal places.
When can you use small change assumption? ›
This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial concentrations. However, to make this assumption, the change in the concentration of a weak acid or base, i.e., x, must be less than 5% of its initial concentration.
The rule states that an acid-base reaction can be approximated if the concentration of the acid or base is at least 100 times greater than the Ka or Kb value.
What is the rule of assumption? ›
The law of assumption states that, by believing the thing you want already exists in your life, you'll manifest it into existence. The law of assumption is a positive thinking tactic created by Neville Goddard as a method of reframing one's outlook.
How to turn ka into pKa? ›
To create a more manageable number, chemists define the pKa value as the negative logarithm of the Ka value: pKa = -log Ka.
What is the 5% rule? ›
It dates back to 1943 and states that commissions, markups, and markdowns of more than 5% are prohibited on standard trades, including over-the-counter and stock exchange listings, cash sales, and riskless transactions. Financial Industry Regulatory Authority (FINRA).
What is pKa? ›
pKa is a number that describes the acidity of a particular molecule. It measures the strength of an acid by how tightly a proton is held by a Bronsted acid. The lower the value of pKa, the stronger the acid and the greater its ability to donate its protons. describe the acidity of a particular molecule.
What is the law of equilibrium? ›
Definitions of equilibrium law. noun. (chemistry) the principle that (at chemical equilibrium) in a reversible reaction the ratio of the rate of the forward reaction to the rate of the reverse reaction is a constant for that reaction. synonyms: law of chemical equilibrium. type of: law, law of nature.
How to check if small x is valid? ›
We must test x to ensure that the small x approximation was a good approximation. If x is within 5% of the number it was being subtracted from (or added to), the small x approximation is good enough. Note: The “5%” threshold is somewhat arbitrary.
What is the small number approximation? ›
The approximation is sometimes called "the law of small numbers" because it approximates the distribution of the number of successes when the chance of success is small: you only expect a small number of successes. As an example, here is the binomial (1000,2/1000) ( 1000 , 2 / 1000 ) distribution.
What is x in an ice table? ›
Let "x" represent the change in concentration of the hydrogen gas. Since we start with HI alone, the reaction must proceed to the right resulting in an increase in the amount of hydrogen gas. Example: 0.600 moles of NO and 0.750 moles of O2 are placed in an empty 2.00 L flask.
What is the difference between big K and little K in chemistry? ›
A large K value (greater than 1) indicates that there are more products than reactants at equilibrium, while a small K value (less than 1) indicates that there are more reactants than products at equilibrium.
