The Volumetric Flask: Density, Significant Figures, and What Counts as a Mixture
During a lab practical, a nursing student is given three items on a tray: a sealed 25.0 mL volumetric flask holding a clear, colorless liquid; a 500 mL bag labeled 0.90% sodium chloride in water; and a beaker of the same salt water that has been boiled down to roughly half its original volume. The empty flask weighed 18.42 g, and the filled flask weighs 44.72 g on the same balance. The instructor states that the reference density for the solution is 1.05 g/mL and warns that 'close enough' is not acceptable - the reported value must carry the correct number of significant figures. The student must also decide whether boiling the salt water is a physical or a chemical change, and whether the bag contains a compound, a heterogeneous mixture, or a homogeneous mixture. A classmate argues that because sodium chloride is a compound, the bag contents must be a compound too.
1. Calculate the density of the flask contents and decide whether the result agrees with the 1.05 g/mL reference. Show how significant figures control the answer.
Read the worked answer
Mass of the liquid (weighing by difference): 44.72 g − 18.42 g = 26.30 g. Both readings were made to the same 0.01 g place on the same balance, so the difference is reported to that place: 26.30 g, four significant figures.
Density: d = m/V = 26.30 g ÷ 25.0 mL = 1.052 g/mL before rounding.
Significant figures: 26.30 has four significant figures (the trailing zero after the decimal counts). 25.0 has three (the 2 and 5 are nonzero, and the trailing zero after the decimal counts). Division keeps the smallest count, so the reported value must have three significant figures: 1.05 g/mL.
Judgment: 1.05 g/mL agrees with the reference at the precision the glassware allows. Reporting 1.052 would claim precision the 25.0 mL flask and the 0.01 g balance cannot support; reporting 1.1 would discard real information. A value like 1.20 g/mL would be a true mismatch, not a rounding artifact.
2. Classify (a) the change that occurs during boiling and (b) the contents of the bag. Respond to the classmate's claim.
Read the worked answer
(a) Boiling is a physical change. Water goes from liquid to vapor and can be condensed back. No new substance forms, and the sodium chloride stays behind. The identity of the components is unchanged; only the state of the water changes.
(b) The bag is a homogeneous mixture (a solution). It holds two substances, NaCl and water, physically combined in a ratio that can vary - 0.45%, 0.90%, and 3% saline are all real products. Each component keeps its own properties, and the components can be separated by physical means such as evaporation or distillation. The sample is uniform throughout, which makes it homogeneous rather than heterogeneous.
(c) The classmate confuses a component with the whole sample. Sodium chloride itself is a compound: sodium and chlorine are chemically bonded in a fixed 1:1 ratio, and separating them requires a chemical change such as electrolysis. But a compound dissolved in water yields a mixture. Classification depends on the entire sample, not on one ingredient in it.
3. The student must enter the density into a database that reports g/L. Convert the value, preserve the significant figures, and explain what goes wrong if the answer is typed as 1050 g/L.
Read the worked answer
1.05 g/mL × (1000 mL / 1 L) = 1050 g/L. The conversion factor 1000 mL/L is exact by definition, so it does not limit significant figures; the value still carries three significant figures inherited from 1.05.
Typed as 1050 g/L, the trailing zero is ambiguous - a reader cannot tell whether it is significant, so the entry could be read as two, three, or four significant figures. The unambiguous form is 1.05 × 10³ g/L, which states three significant figures explicitly.
Do not 'fix' this by rounding to 1.1 × 10³ g/L; that would drop below the precision of the original measurement. The rule to carry away is that unit conversions change the number and the unit but never the significant-figure count, and scientific notation is how that count is protected when trailing zeros are involved.