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Rearranging equations to change the subject

Quantitative chemistry • Volumes of gases

Key concepts

What you'll likely be quizzed about

  • The subject of an equation is the symbol that stands alone on one side of the equals sign.
  • Changing the subject means isolating that symbol, which involves removing other terms that multiply, divide, add, or subtract from the chosen symbol using inverse operations on both sides.
  • The subject becomes the dependent quantity, calculated directly from other symbols.

Flashcards

Test your knowledge with interactive flashcards

How to make n the subject from pV = nRT?

Click to reveal answer

Divide both sides by RT to get n = pV / RT.

Key notes

Important points to keep in mind

Perform inverse operations on both sides to keep the equation balanced.

Reverse the order of operations when isolating the subject.

Convert units to SI when using R = 8.31 in pV = nRT.

Remove denominators by multiplying both sides by the denominator before isolating the variable.

Collect like terms or factorize when the subject appears in multiple terms.

Check rearrangements by substituting numeric values into the original and rearranged equation.

Apply physical limits after algebraic steps (e.g., volume and temperature must be positive).

Use consistent units across all terms to avoid numerical errors.

Reciprocals and roots introduce sign or domain considerations that require context checks.

When using molar gas volumes in dm3, include conversion to m3 when R in SI units is used.

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