3 Ways to Find the Volume in a Test Tube

Finding the volume of a test tube or NMR tube is a common chemistry calculation, both in the lab for practical reasons and in the classroom to learn how to convert units and report significant figures. Here are three ways to find the volume.

Calculate Density Using Volume of a Cylinder

A typical test tube has a rounded bottom, but NMR tubes and certain other test tubes have a flat bottom, so the volume contained in them is a cylinder. You can get a reasonably accurate measure of volume by measuring the internal diameter of the tube and the height of the liquid.

The best way to measure the diameter of a test tube is to measure the widest distance between the inside glass or plastic surfaces. If you measure all the way from edge to edge, you'll include the test tube itself in your measurements, which isn't correct.

Measure the volume of the sample from where it starts at the bottom of the tube to the base of the meniscus (for liquids) or the top layer of the sample. Don't measure the test tube from the bottom of the base to where it ends.

Use the formula for the volume of a cylinder to perform the calculation:

V = pi r^2 h

where V is volume, pi is 3.14 or 3.14159, r is the radius of the cylinder and h is the height of the sample

The diameter (which you measured) is twice the radius (or radius is one-half diameter), so the equation may be rewritten:

V = pi (1/2 d)^2 h

where d is diameter.

Example Volume Calculation

Let's say you measure an NMR tube and find the diameter to be 18.1 mm and height to be 3.24 cm. Calculate the volume. Report your answer to the nearest 0.1 ml.

First, you'll want to convert the units so they are the same. Please use cm as your units, because a cubic centimeter is a milliliter! This will save you trouble when it comes time to report your volume. Continue reading..