Basics of Manipulating Relationships

Knowing how to manipulate relationships and equations is a fundamental skill required in chemistry. Some of the benefits of knowing how to manipulate equations is that it is much easier to 'solve' before inserting numbers and if you can isolate a variable on one of the equation, you only have to remember one equation that has all the variables in it as you can then manipulate it to solve for any other variable.

There are some very basic rules for manipulating equations.

  1. You can add, subtract, and multiply by anything, as long as you do the same thing to both sides of the equal sign. You can also divide by anything except zero, again as long as you do the same thing to both sides of the equals sign. For example, if you add 10 to one you must also add 10 to the other.
  2. To move or cancel a quantity or variable on one side of the equation, perform the "opposite" operation on both sides of the equation.

The following are the steps to solve a typical equation:

  1. Assess what variables and constants (numbers) you have available.
  2. Determine what the question is asking you to calculate. What is the variable you're after?
  3. Rearrange the equation so that the unknown variable is isolate on one side of the equals sign and all other variables and constants are on the other side.
  4. Substitute the numbers in with the known variables.
  5. Calculate the equation and determine the value of the unknown variable.

We will go through some examples in the next part.

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