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I-05: Algebra and scientific equation rearrangement

IntoChemistry | General Chemistry I Math Readiness

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Module I-05 · Recommended before: Before gas laws, density and calorimetry

Algebra and scientific equation rearrangement

Equations describe relationships rather than commands to punch into a calculator. Isolate the requested variable before substituting data.

Learn the method

P V = n R T → T = P V / (n R)

  1. Identify the variable to isolate.
  2. Reverse operations in the correct order.
  3. Keep both sides balanced.
  4. Substitute the values with units.
  5. Check by substituting the answer into the original equation.

Common mistake: Dividing only one term of the numerator or denominator changes the equation.

Worked example

Problem: Rearrange P V = n R T to solve for T.

Step-by-step solution: Divide both sides by n R: T = P V / (n R). Check that the result has kelvin units.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Inverse relationships

From density d = m/V, solve V = m/d. With m = 12.0 g and d = 3.00 g/mL, V = 4.00 mL.

Multiple-variable substitution

Given q = mcΔT, calculate c = q/(mΔT), not c = q/m×ΔT. The entire product mΔT is the denominator.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Given y = 6x + 5, solve for x when y = 17.
Hint for question 1

Subtract the constant term before dividing.

Question 2. Given y = 2x + 6, solve for x when y = 20.
Hint for question 2

Subtract the constant term before dividing.

Question 3. Given y = 3x + 7, solve for x when y = 31.
Hint for question 3

Subtract the constant term before dividing.

Question 4. Given y = 4x + 8, solve for x when y = 44.
Hint for question 4

Subtract the constant term before dividing.

Question 5. Given y = 5x + 9, solve for x when y = 59.
Hint for question 5

Subtract the constant term before dividing.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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