Model a dilution

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Final concentration equals initial concentration times initial liters divided by final liters. Formula: a*b/c. Variable key: a = initial concentration (mol/L), b = initial volume (L), c = final volume (L)
• Distinct worked inputs and result: A distinct model has 1 mol/L in 2 L diluted to 8 L: 1×2/8=0.25 mol/L.
• Assessment case 1: Supplied case 1: initial concentration (mol/L)=2; initial volume (L)=1; final volume (L)=4, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?
• Assessment case 2: Supplied case 2: initial concentration (mol/L)=3; initial volume (L)=2; final volume (L)=6, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?
• Assessment case 3: Supplied case 3: initial concentration (mol/L)=1.5; initial volume (L)=2; final volume (L)=5, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?
• Assessment case 4: Supplied case 4: initial concentration (mol/L)=4; initial volume (L)=1; final volume (L)=8, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?
• Assessment case 5: Supplied case 5: initial concentration (mol/L)=2.5; initial volume (L)=3; final volume (L)=10, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?
• Assessment case 6: Supplied case 6: initial concentration (mol/L)=5; initial volume (L)=2; final volume (L)=20, using the explicitly named quantities. Final concentration equals initial concentration times initial liters divided by final liters. What result follows?

Learn the idea

With the stated solute conserved, initial concentration times volume equals final concentration times volume. Volumes must use the same unit. Actual solution behavior can require more detailed assumptions.

Final concentration equals initial concentration times initial liters divided by final liters. The formula in the supplied model is a*b/c. Variable key: a = initial concentration (mol/L), b = initial volume (L), c = final volume (L). Track conserved solute, not constant concentration. Final volume belongs in the denominator.

A distinct model has 1 mol/L in 2 L diluted to 8 L: 1×2/8=0.25 mol/L. This is a supplied calculation, not mixing instructions. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with initial concentration (mol/L)=3; initial volume (L)=1; final volume (L)=4. Expected result: 0.75 mol/L. Explain what changes and keep this assumption: This is a supplied calculation, not mixing instructions.

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