Recording-2025-01-22T20:05:17.656Z

Algebra in Chemistry

• The principles of algebra apply to chemistry equations, allowing for modifications and isolations of unknowns just as in mathematical equations.

Fundamental Rules of Algebraic Operations in Chemistry

Rule 1: Equality on Both Sides of the Equation

• Whatever operation is performed on one side of an equation must also be performed on the other side.

  • Example: If you multiply one side by 20, you must multiply the other side by 20 as well.

Rule 2: Separating Divided Quantities

• To separate a quantity divided by another, multiply both sides of the equation by the other quantity.

  • Example: For the equation n/150 = 510, isolating n involves multiplying both sides by 150.

Rule 3: Separating Multiplied Quantities

• To separate a quantity that is multiplied by another, multiply both sides of the equation by the reciprocal of the other quantity.

  • If n is multiplied by 2, the equation can be modified by dividing both sides by 2 to isolate n.

Rule 4: Handling Added or Subtracted Quantities

• To remove a quantity that is added to or subtracted from another, add or subtract the negative of that quantity to both sides.

  • Example: a + 20 = 60 requires subtracting 20 from both sides to isolate a.

Example Problems

1. Example 1: Isolating n

   • Starting from n/150 = 5/10:

     • Using cross multiplication results in n = (5 * 150)/10 = 75.

2. Example 2: Isolating n with Multiplication

   • For the equation 2n = 50, divide both sides by 2 to find n = 25.

3. Example 3: Isolating a

   • For a + 20 = 60, subtract 20 from both sides to solve for a.

Practical Application: Density Formula

• Density is defined as mass over volume (Density = mass/volume).

• To isolate mass (m), rearranging the equation gives: m = Density × Volume.

• This allows for straightforward calculations when density and volume are known.