Source: CHEM 106 Lab Report, New York University
Tags: mixture density, conservation of volume, conservation of mass, hydrogen bonding, ethanol-water mixture, volume contraction, miscible, CHEM 106
Difficulty: Introductory | Prerequisites: Density, Volume, and Measurement study notes (Part 1 of this set)
This is the second half of the density lab, and it tackles a question most students get wrong on the first try: when you mix two liquids, is the total volume simply the sum of the two individual volumes? For water and ethanol the answer is no, and the reason has to do with how molecules arrange themselves at the molecular level. Understanding this teaches you that macroscopic measurements (what you see in the cylinder) reflect molecular-scale events (hydrogen bonding and packing), which is one of the core ideas in general chemistry.
When you mix water and ethanol, mass is always conserved but volume is not. The total volume of the mixture is less than the sum of the two individual volumes because ethanol molecules tuck into gaps in water's hydrogen-bonding network. This volume contraction means the experimental density of a water-ethanol mixture is higher than what you would calculate by simply averaging the two pure densities.
Conservation of mass
Mass cannot be created or destroyed in an ordinary physical or chemical process. When you mix 10 g of water with 5 g of ethanol, you get 15 g of solution, always. Think of it as: the molecules are still all there, they have just rearranged.
Conservation of volume (or lack thereof)
Volume is not necessarily conserved when two substances are mixed. 10 mL of water plus 10 mL of ethanol gives roughly 19.1 to 19.8 mL of solution, not 20 mL. In simple terms, the molecules pack more tightly together than they did in their separate containers.
Hydrogen bonding
An intermolecular force between a hydrogen atom bonded to an electronegative atom (O, N, F) and a lone pair on another electronegative atom. Both water and ethanol form hydrogen bonds, which is why they are miscible and why their molecules can interleave and pack closely.
Molecular packing
How molecules arrange themselves relative to one another in a liquid. When ethanol and water mix, the smaller water molecules fit into spaces between ethanol molecules, reducing the total volume. This is the molecular-level explanation for volume contraction.
Volume percent (% v/v)
The volume of a component divided by the total volume of the mixture, multiplied by 100. In this lab, the starting volumes (before mixing) are used to define the composition.
Expected density (ideal mixing)
The density you would predict if volumes were perfectly additive and no contraction occurred. Calculated from the weighted average of the pure component densities.
Experimental density
The density measured directly from the mixture using mass divided by the actual (observed) volume.
Seven mixtures were prepared at different water-to-ethanol volume ratios: 16:4, 12:8, 10:10, 8:12, 4:16, plus pure water (10:0) and pure ethanol (0:10).
For each mixture, the mass of the solution was measured and the volume of the resulting mixture was recorded.
Two trials were run per mixture to check reproducibility.
The key observation: when you combine, say, 10 mL of water with 10 mL of ethanol, the resulting solution volume is approximately 19.1 to 19.7 mL, not 20 mL.
This shortfall (roughly 0.3 to 0.9 mL) is consistent across all mixtures.
The missing volume is not lost matter. The mass of the mixture equals the sum of the masses of its components (conservation of mass holds perfectly). It is the space that shrinks.
Water molecules are small and form an open, tetrahedral hydrogen-bonding network with considerable empty space.
Ethanol molecules (CH₃CH₂OH) are larger but have a hydroxyl group (-OH) that hydrogen-bonds with water.
When mixed, ethanol's -OH group slots into water's hydrogen-bonding network, and ethanol's hydrocarbon tail occupies gaps that were previously empty space.
The net effect: the molecules pack more efficiently together than either does on its own, so the total volume decreases.
The expected (ideal) density assumes volumes are additive. It is calculated from a weighted average of the pure component densities.
Experimental densities were consistently higher than expected densities in this lab.
This makes sense: if the actual volume is smaller than expected but the mass is the same, then mass/volume gives a larger number.
For example, at roughly 52% water and 48% ethanol by volume, the experimental density was 0.91 g/mL while the expected density was considerably lower.
As the fraction of ethanol increases, the mixture density decreases. Ethanol is less dense than water, so more ethanol means a lighter mixture per unit volume.
The graph from the lab shows this as a downward trend from about 0.94 g/mL (20% ethanol) to 0.87 g/mL (83% ethanol).
Pure water gave an experimental density of about 1.35 g/mL in this lab (notably higher than the accepted 1.00 g/mL, suggesting a measurement error in that particular trial).
Pure ethanol gave about 1.24 g/mL experimentally (also higher than the accepted 0.789 g/mL, again suggesting systematic error in those trials).
Volume percent:
\text{Volume \%} = \frac{V_{\text{component}}}{V_{\text{total (before mixing)}}} \times 100Expected (ideal) density of a mixture:
\rho_{\text{expected}} = \frac{m_{\text{water}} + m_{\text{ethanol}}}{V_{\text{water}} + V_{\text{ethanol}}}Where each mass is calculated from the pure density times the volume used (m = ρ x V).
Percent error:
\text{\% error} = \frac{|\text{experimental} - \text{accepted}|}{\text{accepted}} \times 100Use this to compare your measured density against a literature or expected value.
Volume contraction in ethanol-water mixtures is why the spirits industry measures alcohol content by volume percent at a standard temperature, not by simply mixing volumes. A distiller who adds 500 mL of pure ethanol to 500 mL of water does not get 1,000 mL of product.
The same principle applies in pharmacy when compounding solutions. Pharmacists must account for volume changes when mixing solvents, because dosing depends on accurate concentrations.
Students often assume that if you mix 10 mL of liquid A with 10 mL of liquid B, you get exactly 20 mL. This is true for ideal mixtures (some gas mixtures, for instance) but not for water and ethanol, or most pairs of miscible liquids with strong intermolecular interactions.
Some students confuse conservation of mass with conservation of volume. Mass is always conserved in mixing. Volume is not. These are different physical quantities governed by different principles.
A common error is thinking the volume decreases because matter is destroyed. No matter is lost. The molecules simply occupy less total space because they pack more efficiently.
Students sometimes believe that because gases have no fixed volume, volume is never conserved for gases either. In an open container that is correct, but in a sealed container at constant temperature, gas volumes can be additive (Dalton's law context). The answer depends on conditions.
⚠️ The distinction between conservation of mass and conservation of volume is a favourite exam question. Be ready to state clearly that mass is always conserved but volume is not when miscible liquids with hydrogen bonding are mixed.
⚠️ You may be asked to predict what happens when 1-propanol (or another alcohol) is mixed with water. The answer follows the same logic: mass is conserved, volume is not, because hydrogen bonding causes molecular packing.
⚠️ Expect a question asking you to use a density-vs-composition graph to predict the density of a mixture at a given percent ethanol. From this lab's graph, a 43% ethanol solution has an experimental density of roughly 0.90 g/mL.
⚠️ Explaining why experimental density exceeds expected density is a common short-answer prompt. The answer: volume contraction means the measured volume is less than the sum of component volumes, so mass/volume yields a higher number than the ideal calculation predicts.
True or false: When you mix water and ethanol, the total mass is less than the sum of the individual masses. (False. Mass is always conserved.)
True or false: 10 mL of water plus 10 mL of ethanol yields exactly 20 mL of solution. (False. Volume is not conserved; the result is less than 20 mL.)
Fill in the blank: The volume of a water-ethanol mixture is less than the sum of the components because of ______ between molecules. (Hydrogen bonding / molecular packing)
True or false: Experimental density of a water-ethanol mixture is typically lower than the expected density. (False. It is typically higher, because the actual volume is smaller than expected.)
Fill in the blank: A property that does not change with sample size is called an ______ property. (Intensive)
Q: When you mix alcohol and water, is volume conserved? Explain using the concept of molecular packing.
A: No. Volume is not conserved. Water and ethanol are miscible, and when mixed, ethanol's hydroxyl group hydrogen-bonds with water while its hydrocarbon tail fills gaps in water's open hydrogen-bonding network. This tighter molecular packing reduces the total volume below the sum of the individual volumes.
Q: If 1-propanol is mixed with distilled water, are mass and volume conserved?
A: Mass is conserved (mass cannot be created or destroyed in a physical process). Volume is not conserved, for the same reason as ethanol and water: 1-propanol forms hydrogen bonds with water, leading to more efficient molecular packing and a volume contraction.
Q: When you mix two gases in a sealed container, is volume conserved?
A: In a sealed rigid container the volume of the container does not change, but the gas fills whatever volume is available. Gases do not have a definite volume of their own. If more gas is added to a sealed container, pressure increases rather than volume. In an open system, gas volumes can be roughly additive (Dalton's law context) assuming ideal behaviour.
Q: Hydrogen gas burns with oxygen to form liquid water. What can you say about conservation of mass and volume?
A: Mass is conserved: the total mass of reactants equals the total mass of products. Volume is not conserved: the reactants are gases (large volume) and the product is a liquid (much smaller volume), so the total volume decreases dramatically.
Q: Using a density-vs-composition graph, predict the density of a 43% ethanol solution in water.
A: From the experimental trendline, the density at 43% ethanol is approximately 0.90 g/mL.
Q: Why are the experimental densities of water-ethanol mixtures higher than the expected (ideal) densities?
A: Because the actual volume of the mixture is smaller than the sum of the component volumes (volume contraction from hydrogen bonding). Since density = mass / volume, a smaller denominator with the same numerator gives a larger density value.
This connects directly to intermolecular forces (Chapter 11 in most general chemistry textbooks). The hydrogen bonding that causes volume contraction here is the same force that explains water's unusually high boiling point, surface tension, and heat capacity.
The concept of ideal vs. non-ideal mixing appears again when you study solutions and colligative properties. An ideal solution obeys Raoult's law; the water-ethanol system deviates from it, which is why distilling alcohol to high purity is difficult (it forms an azeotrope).
Conservation of mass is a preview of stoichiometry, where you will balance equations by ensuring the same number of atoms appear on both sides.
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