The Amazing World of Solutes, Solvents, and Solutions · Lesson 4 of 7
Measuring Mass and Liquid Volume
“Learn to tare a balance and read a measuring cylinder so your measurements support reliable calculations.”
• Distinguish mass from weight and state their units. • Measure sample mass using zeroing and taring. • Convert between litres, millilitres, and cubic centimetres. • Choose a measuring cylinder using capacity and scale division. • Read a meniscus at eye level and explain common measurement errors.
Two Measurements for Finding Density
A density formula is useful only when the mass and volume are reliable. A balance can accidentally include the mass of a container, and a cylinder can give a misleading reading if viewed from the wrong height. This lesson develops the instrument skills needed before we combine measurements in the next lesson.
Mass is the quantity of matter in an object. A balance gives a mass reading in grams or kilograms. Weight is different: it is the force with which gravity pulls on the object, measured in newtons. Many electronic scales sense a force and are calibrated to display mass under ordinary conditions. A scale labelled in grams is giving you a mass value for these calculations.
The quantity of matter in an object, commonly measured in grams (g) or kilograms (kg).
The gravitational force acting on an object, measured in newtons (N).
Zeroing and Taring a Balance
Before measuring, the balance must display zero for the condition you want to exclude. Zeroing an empty balance corrects its starting reading. Taring after placing a container on it excludes that container so that the next reading gives the sample mass alone.
For the stone investigation, switch on the balance and check the empty reading. If it is not zero, use the zero control. Put a clean, dry watch glass or suitable paper on the pan. Press tare so the display returns to zero with that support still in place. Add the stone carefully and record the displayed mass, including its unit. A reading such as 16.400 g belongs to the stone alone after correct taring.
To measure a liquid, use a suitable beaker instead of the watch glass. Place the empty, dry beaker on the balance, tare it, and add the liquid carefully. The reading is the mass of the liquid. Keep spills off the balance and choose a container large enough for the sample. A two-pan balance can also measure mass by comparing the sample with known masses.
Problem
An empty beaker is placed on a balance and tared. After water is added, the display reads 75.0 g. What is the water’s mass?
- 1.Taring made the empty beaker the zero reference.
- 2.The 75.0 g reading therefore excludes the beaker mass.
- 3.The mass of water is 75.0 g. Do not subtract the beaker mass again.
Problem
A beaker has mass 42 g. The beaker and liquid together have mass 118 g. Find the liquid’s mass.
- 1.The combined reading includes both container and liquid.
- 2.Subtract the known empty-container mass: 118 g − 42 g = 76 g.
- 3.The liquid’s mass is 76 g. Taring the empty beaker would have given this sample-only reading directly.
A balance does not know which material you intend to study. Either tare the empty container or subtract its measured mass. Keep the same container and do not remove a tared support before taking the sample reading.
Volume Units and Measuring Cylinders
Volume tells us how much space is occupied. A package labelled 200 mL describes the volume of its contents rather than their mass. For liquids, graduated measuring cylinders let us read volume directly from a scale.
The standard international volume unit is the cubic metre, m³. Smaller volumes are often expressed in cubic decimetres or cubic centimetres. Liquid volumes commonly use litres and millilitres. A litre equals a cubic decimetre, while a millilitre equals a cubic centimetre. You may also see cm³ described as cc.
| Volume relationship | Useful interpretation |
|---|---|
| 1 L = 1 dm³ | A litre is the volume of a cube 1 dm on each edge. |
| 1 L = 1000 mL | Convert litres to millilitres by multiplying by 1000. |
| 1 mL = 1 cm³ | A millilitre occupies one cubic centimetre. |
| 200 mL = 0.2 L = 200 cm³ | Three descriptions of the same liquid volume. |
A measuring cylinder is a narrow container with a scale showing volume. Its capacity is the largest volume it is designed to measure. Its smallest scale division is the volume represented by one small interval between adjacent scale lines. These two features answer different questions: can it hold the required amount, and how finely can you read it?
The volume difference represented by one interval between adjacent scale lines on the instrument.
Reading the Scale and Choosing an Instrument
Do not assume that all cylinders have the same scale. Examine the labelled values and count the intervals between them. A smaller interval usually allows a finer reading, but the cylinder must still have enough capacity for the required volume.
Problem
A cylinder has labels at 40 mL and 50 mL with ten equal intervals between those labelled lines. What volume is one interval?
- 1.Find the labelled difference: 50 − 40 = 10 mL.
- 2.Divide by the number of intervals: 10 mL ÷ 10 = 1 mL per interval.
- 3.Count the spaces between lines, not just the number of lines. One interval represents 1 mL.
For the cylinder investigation, identify its maximum labelled capacity and record two neighbouring large scale values. Count the small intervals between them and calculate the volume of one interval. Cylinders come in capacities such as 5, 10, 25, 50, 100, and 250 mL. Some small cylinders permit readings in 0.1 mL divisions; a 100 mL cylinder may have 1 mL divisions, and larger ones may have 2 mL or 5 mL divisions. Check the actual instrument, because capacity does not guarantee one universal scale spacing.
Problem
You have cylinders of 50 mL, 100 mL, 250 mL, and 500 mL capacity. Their divisions are respectively 1 mL, 1 mL, 2 mL, and 5 mL. Which is most suitable for measuring 70 mL in one reading?
- 1.A 50 mL cylinder cannot hold 70 mL at once; measuring in two transfers adds opportunities for error.
- 2.The 250 mL and 500 mL cylinders hold enough, but their stated scales are coarser.
- 3.The 100 mL cylinder holds 70 mL and has a fine enough stated scale. Choose it for this task, while remembering to inspect real instruments before choosing.
The narrow, tall shape of a cylinder helps separate volume levels visibly: in a narrower container, the same small added volume produces a larger rise in liquid height. A wide beaker is useful for holding and mixing but its volume readings are usually less precise. The opening question about bottle shapes also invites thinking about handling, storage, and design; bottle shape alone does not make a bottle a measuring instrument.
Measuring 50 mL and Reading the Meniscus
Water in a measuring cylinder has a curved surface called a meniscus. The lowest point of that curve gives the usual reading for water and other clear liquids with a similar concave surface. Looking from above or below can make the level appear to match the wrong scale line.
Place a clean cylinder upright on a flat surface. Pour water slowly until it is near 50 mL. Use a dropper to add or remove small amounts for the final adjustment. Lower your eyes to the same height as the bottom of the water meniscus, then read the line aligned with it. Keep the cylinder on the surface rather than tilting it toward your face.
For water, read the bottom of the concave meniscus. If a strongly coloured liquid hides that bottom, some school procedures specify the visible upper edge; follow the procedure supplied for the liquid and instrument. Colour alone is not a universal rule that changes the physical meniscus. Record the convention used.
Quiz
Which statement correctly distinguishes mass and weight?
Why is an empty container tared before adding a sample?
There are five equal intervals from 20 mL to 30 mL. What is one interval?
Which equals 200 mL?
Where should your eye be when reading water in a measuring cylinder?
Practice Problems
- Describe how to measure a stone’s mass with a watch glass and a digital balance. Explain the purpose of both the initial zero check and tare.
- An empty beaker has mass 35 g; with a liquid it has mass 127 g. Calculate the liquid mass. What would a correctly tared balance display?
- Convert 0.75 L to mL and cm³. Convert 250 mL to litres.
- A scale has four equal intervals between 60 mL and 80 mL. Find the smallest division and explain why intervals, rather than lines, must be counted.
- Choose an instrument to measure 90 mL in one reading from cylinders of 50 mL, 100 mL, and 500 mL with respective divisions of 1 mL, 1 mL, and 5 mL. Justify the choice.
- Explain how to adjust a water sample to 50 mL and why viewing the meniscus from above is a source of error.
- Explain why a narrow measuring cylinder can show a small volume change more clearly than a wide beaker.
Key Takeaways
• Mass is measured in g or kg; weight is a force measured in N. • Zero the balance, then tare a suitable empty container to obtain sample mass alone. • 1 L = 1000 mL and 1 mL = 1 cm³. • Cylinder capacity and smallest division are different properties; inspect both. • Calculate one division by dividing the labelled volume difference by the number of intervals. • Read water at the bottom of its meniscus with the cylinder upright and your eye at that height.