Mass, volume, temperature and density

Mass and volume ask different questions

Mass and volume are distinct quantities. A balance provides a mass indication using its measurement principle and calibration. Weight is a force associated with gravity; its SI unit is the newton, while the kilogram is a mass unit. In an ordinary laboratory report, state the measured mass rather than silently switching between mass and force.

Volume describes three-dimensional extent. A liquid volume reading depends on the apparatus and the reading method. A graduated vessel and a calibrated volumetric vessel serve different purposes. For a real measurement, follow the apparatus method, including its temperature conditions and how the liquid boundary is read. The smallest printed graduation is not a complete uncertainty estimate.

Use mass and volume from the same sample

Density is mass divided by volume:ρ=m/V. The Greek letterρ, pronounced rho, names density; m is mass and V is volume. An invented sample has an indicated mass of 18.0 g and volume of 6.0 mL. Its calculated density is 18.0/6.0=3.0 g/mL. The ratio concerns that sample under the recorded conditions.

If you double the amount of a uniform material without changing its conditions, both mass and volume double and the density stays the same. This describes a suitable uniform sample, not every mixture or object with pores. Distinguish the material’s density from a bulk density that includes spaces between grains. Always ask which volume was included.

Temperature scales need an offset

For a temperature reading of 20.0 °C, adding the exact 273.15 offset gives an unrounded conversion of 293.15 K. Reporting at the original 0.1-degree resolution gives about 293.2 K; retain the original measurement uncertainty. The scale relation is T/K=t/°C+273.15. Kelvin is written K, without a degree sign. Celsius and kelvin temperature intervals have the same size: a rise of 5 °C is a rise of 5 K. Their zero points differ.

The 273.15 offset is exact; a temperature reading of 20.0 °C is still a measurement with limited precision and uncertainty. Do not invent additional measurement confidence simply because a conversion produces more digits. Also distinguish temperature from heat: temperature describes thermal state; heat is energy transferred because of a temperature difference.

Density is evidence with conditions

Temperature and pressure can affect density, especially for gases. A useful density value therefore includes the substance or sample, phase and relevant conditions. A table entry for one temperature should not be treated as a universal property under every circumstance. Changes in composition or internal porosity can matter too.

A measured density close to a reference value can support an identification, but it seldom proves identity by itself. Different materials can have similar densities, and mixtures may reproduce the same ratio. Combine density with other appropriate evidence and the measurement uncertainty. The arithmetic, the measurement and the identity claim are separate steps.

Worked examples

Try it yourself

1. Which is a mass unit: kilogram or newton?

   Show the answer and reasoning

   Kilogram.

   The newton is a force unit. Mass and gravitational force are related but are different quantities.

2. Calculate density from 15 g and 5 mL.

   Show the answer and reasoning

   3 g/mL.

   Divide mass by the volume of the same sample.

3. Convert the Celsius scale-zero point, 0 °C, to kelvin. Does it mean zero absolute temperature?

   Show the answer and reasoning

   273.15 K; it does not mean zero absolute temperature.

   Celsius and kelvin have different zero points. A Celsius-to-kelvin conversion adds the exact offset.

4. A sample’s density matches one reference entry. Is its chemical identity thereby proven?

   Show the answer and reasoning

   No.

   Other materials or mixtures can have similar densities, and conditions and uncertainty need checking.

What to carry forward

• Mass, force, volume and temperature name different quantities.
• Density uses matched mass and volume for a stated sample and conditions.
• Celsius-to-kelvin conversion adds an exact offset.
• A property measurement can support identity without uniquely establishing it.