Density of Irregular Solids

General Chemistry • Matter Its Properties and Measurement

Written by STEM Calculators Team Published October 9, 2025 Updated February 24, 2026

Choose the method and what to solve for. Chemistry-friendly inputs are provided (g, mL, g·mL\(^{-1}\)); results are also shown in SI (\(\mathrm{kg\cdot m^{-3}}\), \(\mathrm{kg}\), \(\mathrm{m^{3}}\)).

Method Solve for

Mass \( m_s \)

Density \( \rho_s \)

Graduated cylinder readings

Initial volume \( V_i \) \([\mathrm{mL}]\)

Final volume \( V_f \) \([\mathrm{mL}]\)

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Density of Irregular Solids

Density of a solid is

\[ \begin{aligned} \rho_s &= \frac{m_s}{V_s} \end{aligned} \]

For irregular bodies in chemistry labs, \(V_s\) is determined by liquid displacement: either the graduated-cylinder method or the pycnometer (density bottle) method. Long equations are shown vertically to remain readable on small screens.

1) Liquid displacement (graduated cylinder)

\[ \begin{aligned} V_s &= V_f - V_i \\ &\text{(readings in mL)} \end{aligned} \] Then \[ \begin{aligned} \rho_s &= \frac{m_s}{V_s} \end{aligned} \]

Ensure the object is fully submerged (use a sinker if it floats) and remove trapped air bubbles. Unit conversions (vertical form to avoid width):

\[ \begin{aligned} 1\ \mathrm{mL} &= 1\times 10^{-6}\ \mathrm{m^{3}} \\ 1\ \mathrm{g\cdot mL^{-1}} &= 1000\ \mathrm{kg\cdot m^{-3}} \end{aligned} \]

2) Pycnometer (density bottle)

Measure masses in grams: \(m_0\) (empty), \(m_1\) (filled with liquid), \(m_2\) (solid + liquid), \(m_s\) (solid).

\[ \begin{aligned} m_{\text{disp}} &= (m_1 - m_0) - (m_2 - m_0 - m_s) \\ &= m_1 - m_2 + m_s \end{aligned} \] \[ \begin{aligned} V_s &= \frac{m_{\text{disp}}}{\rho_\ell} \end{aligned} \] \[ \begin{aligned} \rho_s &= \frac{m_s}{V_s} \\ &= \rho_\ell \cdot \frac{m_s}{\,m_1 - m_2 + m_s\,} \end{aligned} \]

Assumptions: solid is insoluble and non-reactive in the liquid; pores are either fully dry and non-penetrated or fully wetted (be consistent); temperature matches the tabulated \(\rho_\ell\). Dry the bottle exterior before each weighing.

Reporting results

\[ \begin{aligned} \rho_s(\mathrm{kg\cdot m^{-3}}) &\quad\text{and}\quad \rho_s(\mathrm{g\cdot mL^{-1}}) \end{aligned} \]

Use significant figures consistent with your balance and volume-reading precision.

Frequently Asked Questions

How do you find the volume of an irregular solid using water displacement?

Measure the liquid volume before and after submerging the solid. The solid volume is Vs = Vf - Vi, assuming full submersion and no trapped air bubbles.

What formula is used to calculate density for an irregular solid?

Density is computed as rho = m / V. The calculator determines V from displacement (Vf - Vi) or from pycnometer measurements combined with the liquid density.

Why do air bubbles or floating objects change the density result?

Bubbles and incomplete submersion change the displaced volume, which changes V and therefore rho. Remove bubbles and ensure the solid is fully submerged for accurate results.

When should a pycnometer method be used instead of a graduated cylinder?

Use a pycnometer when higher precision is needed or when volume readings are difficult to measure accurately. It relies on mass differences and a known liquid density rather than meniscus readings.

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