   # A common type of reaction we will study is that having a very small K value ( K &lt;&lt; 1). Solving for equilibrium concentrations in an equilibrium problem usually requires many mathematical operations to be perfomed. However, the math involved when solving equilibrium problems for reactions having small K values (K &lt;&lt; 1) is simplified. What assumption is made when solving the equilibrium concentrations for reactions with small K values? Whenever assumptions are made, they must be checked for validity. In general, the “5% rule” is used to check the validity of assuming x (or 2 x , 3 x, and so on) is very small compared to some number. When x (or 2 x . 3x. and so on) is less than 5% of the number the assumption was made against, then the assumption is said to be valid. If the 5% rule fails, what do you do to solve for the equilibrium concentrations? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 12, Problem 8RQ
Textbook Problem
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## A common type of reaction we will study is that having a very small K value (K << 1). Solving for equilibrium concentrations in an equilibrium problem usually requires many mathematical operations to be perfomed. However, the math involved when solving equilibrium problems for reactions having small K values (K << 1) is simplified. What assumption is made when solving the equilibrium concentrations for reactions with small K values? Whenever assumptions are made, they must be checked for validity. In general, the “5% rule” is used to check the validity of assuming x (or 2 x, 3x, and so on) is very small compared to some number. When x (or 2 x. 3x. and so on) is less than 5% of the number the assumption was made against, then the assumption is said to be valid. If the 5% rule fails, what do you do to solve for the equilibrium concentrations?

Interpretation Introduction

Interpretation: It is given that for a common type of reaction the value of K<<1 . The assumption made when solving the equilibrium concentrations for reactions with small K values and the procedure followed if the ‘ 5% rule’ fails are to be stated.

Concept introduction: If the error in the equilibrium concentration calculated is less than 5% , the assumption made is stated to be correct. This is known as the ‘ 5% rule’. If the error exceeds the 5% value, then the quadratic formula is used for calculating the equilibrium concentrations.

To determine: The assumption made when solving the equilibrium concentrations for reactions with small K values and the procedure followed if the ‘ 5% rule’ fails.

### Explanation of Solution

On solving the equilibrium concentrations for reactions with small K values, the change in the reactant concentration is taken as negligible. This is the assumption made in solving these kinds of problems

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