Chemistry · General chemistry · Worked example
Convert a mass using density
A sample occupies 25.0 mL and has density 1.20 g/mL. What is its mass?
List what is given and what we need
The sample volume is 25.0 mL and its density is 1.20 g/mL. We want mass in grams. Assume the quoted density applies to this sample under the conditions of the measurement.
Use the meaning of density
Density tells us the mass of each unit of volume. Here, each milliliter contributes 1.20 g. Multiplying that mass per milliliter by the number of milliliters gives the total mass.
Arrange the factors and cancel the units
Put mL in the denominator of the density factor, opposite the mL in the starting quantity. The matching volume units cancel, leaving grams. On the board, use the factor-chain object to select that cancellation yourself.
Calculate the mass
Multiply 25.0 by 1.20. The denominator value 1 only expresses the “per milliliter” part of the density; it does not introduce a measurement with one significant figure.
Report the precision and check the scale
Both measured inputs have three significant figures, so report 30.0 g. Since the density is slightly above 1 g/mL, the mass should be slightly above 25 g. Our result passes that check.
Result
The mass is 30.0 g.
Your turn
A 40.0 mL sample has density 0.850 g/mL. What is its mass? Show the units and report the appropriate significant figures.
Show the answer and explanation
The mass is 34.0 g.
Multiply 40.0 mL by 0.850 g/mL. The mL units cancel, leaving grams. Both measurements have three significant figures. A density below 1 g/mL also tells us to expect a mass below 40 g.
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