Question

Assume that you have two graduated cylinders, one with a capacity of \(5 \mathrm{~mL}\) (a) and the other with a capacity of \(50 \mathrm{~mL}\) (b). Draw a line in each showing how much liquid you would add if you needed to measure \(2.64 \mathrm{~mL}\) of water. Which cylinder do you think is more precise? Explain.

Short answer

Graduated cylinder a is more precise for measuring 2.64 mL of water.

Step-by-step solution

Understanding the Measurement

First, let's understand that we need to measure 2.64 mL of water using two graduated cylinders. Graduated cylinders a and b have capacities of 5 mL and 50 mL respectively.

Reading the Scales

Graduated cylinder a is smaller in capacity, which means it likely has more graduation marks for smaller volumes compared to cylinder b. This allows for more precise measurement at smaller volumes.

Graduated Cylinder a Measurement

On the 5 mL graduated cylinder, locate the scale or markings that indicate 2.6 mL and 0.04 mL. Since smaller increments are easier to read on a smaller cylinder, fill to a precise point between 2.6 and 2.7 for 2.64 mL.

Graduated Cylinder b Measurement

On the 50 mL graduated cylinder, find the mark closest to 2.64 mL. It may be less precise due to larger volume capacity and fewer graduation increments in this range. You might have to estimate as it may be marked only for whole mL increments.

Precision Conclusion

Graduated cylinder a, with its smaller total volume and likely more frequent graduations, will allow a more precise measurement of 2.64 mL compared to cylinder b, which is better suited for larger volumes.

Key concepts

Measurement Precision

Measurement precision is all about how finely we can pinpoint a specific measurement. In our case, it's about how accurately we can determine that we have exactly 2.64 mL of water.

When it comes to measuring liquids in graduated cylinders, a more precise measurement is achieved when the tool you're using has more detailed increments or graduation marks. Imagine a ruler that only marks every inch versus one that marks every eighth of an inch. The second ruler provides more precise measurements.

• Smaller increments mean more detail and accuracy.
• More graduation marks allow you to better estimate fractions or decimal points between the intervals.

So, for finely tuned measurements, a graduated cylinder with closer increment marks gives you greater precision, as it helps pinpoint exactly where that 2.64 mL line will be.

Volume Measurement

Volume measurement is the process of determining the quantity of liquid in a container. For identifying 2.64 mL of water, you have to observe the meniscus, the curved surface of the liquid, as it tends to dip slightly due to surface tension and adhesion.

To measure volume accurately:

• Ensure the graduated cylinder is on a flat surface.
• Look at the meniscus at eye level.
• Read the value from the bottom of the meniscus, not the sides.

Using these steps ensures that your volume measurement is correct. Graduated cylinders are especially useful because they offer clear and simple volume scales marked on the side for easy reading.

Graduated Cylinder Scales

Graduated cylinder scales are the lines drawn on the side of the cylinder that mark volumes. These scales can vary in how frequently they are marked, which affects the precision.

For instance, the 5 mL graduated cylinder mentioned has likely more detailed scales (more graduation lines) than the larger 50 mL cylinder, allowing for better precision.

• Small graduated tubes have fine scales for detailed measurements.
• Larger cylinders offer convenience for measuring greater volumes but at the cost of precision.

The choice of cylinder depends on the precision needed for the measurement. For example, to measure 2.64 mL, the 5 mL cylinder would likely be marked to accommodate such a small volume precisely, while the 50 mL might not. Understanding these scales empowers you to choose the right tool for the job.