# How to calculate changes in solution concentrations

What is the concentration of sodium chloride after 30.0 mL of a 0.25 M solution of sodium chloride is diluted to 0.5L using purified water ?

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Solution:

Short answer: 0.015M

Long answer: (This long answer is very long, but it is worth the read. The long answer will show you how to use the equation, give you some general exam tips, demonstrate common errors that students make when using this equation (and how to catch/avoid those errors), and also shows solutions for a variation of the original question to further demonstrate how the equation can be used to answer test/lab questions.)

Many students of chemistry, biology, and biochemistry (and even many scientists in the workplace!) struggle when faced with problems that require calculating change in concentration. Almost all of these types of problems can be solved by using one simple equation - MEMORIZE IT NOW & USE IT OFTEN! The equation is shown here, and in spoken terms is often referred to as "c one v one equals c two v two".

(C1)(V1) = (C2)(V2)

Where:

C1 = the starting concentration

V1 = the starting volume

C2 = the final concentration

V2 = the final volume.

Now that you've memorized this equation, the key to using the equation successfully is to follow one rule pertaining to UNITS:

As long as all units for "C" are the same, and all units for "V" are the same, this equation can be used with any type of concentration or volume unit. The catch...if the units for C1 and C2 are different, you will get the wrong answer! (Likewise for V1 and V2.)

Confusing? The following examples of incorrect calculations highlight common mistakes. Several versions of the correct calculation are also shown to teach you how you would overcome these mistakes. There are additional comments related to reasoning - by looking at the number you have calculated, and comparing it to the original question, you can often tell whether you have made a costly mistake...before it's too late to change your answer!

Study these examples, memorize the equation, and keep your units consistent!

Original Question: What is the ...

#### Solution Summary

Many students of chemistry, biology, and biochemistry (and even many scientists in the workplace!) struggle when faced with problems that require calculating change in concentration. Almost all of these types of problems can be solved by using one simple equation.

This solution walks you through a four page, step by step summary of how to use the equation (C1V1=C2V2) to answer the problem, but also details common mistakes students make when using the equation, provides exam tips for checking whether you have used the equation correctly before you hand your paper in, and includes "variations" of the original question (with complete step by step solutions).