Question

A Class A 10-mL pipet has an uncertainty of \(\pm 0.01 \mathrm{~mL}\). Express the volume of the pipet as an ordinary number.

Short answer

The pipet volume is from 9.99 mL to 10.01 mL.

Step-by-step solution

Understand the problem

The problem requires us to express the volume of a Class A 10-mL pipet, considering its uncertainty of \(\pm 0.01 \mathrm{~mL}\), as an ordinary number. This means providing the range of possible volumes taking into account the uncertainty.

Identify the Range of Volumes

The nominal volume of the pipet is 10 mL. With an uncertainty of \(\pm 0.01 \mathrm{~mL}\), the actual volume can range from \(10.00 - 0.01\) mL to \(10.00 + 0.01\) mL.

Calculate the Minimum Volume

Subtract the uncertainty from the nominal volume to find the minimum volume: \[ 10.00 \mathrm{~mL} - 0.01 \mathrm{~mL} = 9.99 \mathrm{~mL} \]

Calculate the Maximum Volume

Add the uncertainty to the nominal volume to find the maximum volume: \[ 10.00 \mathrm{~mL} + 0.01 \mathrm{~mL} = 10.01 \mathrm{~mL} \]

Express the Volume as an Ordinary Number

Considering the uncertainty, the volume of the pipet can be expressed as an ordinary number range: \[ 9.99 \mathrm{~mL} \text{ to } 10.01 \mathrm{~mL} \]

Key concepts

Uncertainty in Measurements

When we talk about measurements in scientific contexts, it's crucial to understand that there is almost always some degree of uncertainty involved. It is impossible to have perfectly precise measurements due to limitations in measurement tools and external factors. This uncertainty is usually expressed in terms of a range, indicating the highest and lowest possible values. For the Class A 10-mL pipet mentioned, we have an uncertainty of \(\pm 0.01\, \mathrm{mL}\).

This means that the actual volume could be slightly above or below the pipet’s nominal value, here 10.00 mL. This slight variance in measurement is critical to acknowledge as it affects calculations and results in scientific experiments.

• Ensures accuracy in experiments.
• Helps gauge the precision of instruments.
• Allows scientists to provide a more honest depiction of data.

Understanding and calculating measurement uncertainty helps scientists and engineers maintain high precision levels in their work.

Pipet Volume Range

A pipet is a common laboratory tool used for measuring and transferring precise amounts of liquid. In chemistry, especially, ensuring the accuracy of liquid measurements is vital for the success of any experiment. The range of volume for any pipet is determined by its nominal volume and the associated uncertainty.

For instance, with our Class A 10-mL pipet, the nominal volume is 10.00 mL. Considering the uncertainty of \(\pm 0.01\, \mathrm{mL}\), the actual usable volume range of this pipet becomes 9.99 mL to 10.01 mL.

Such a range informs how much liquid you can confidently assume you’re using, thereby aiding in precise and effective scientific measurements. Moreover, understanding pipet volume ranges helps in:

• Preventing significant errors in experimental results.
• Ensuring consistency and reproducibility in experiments.

Recognizing the pipet's volume range is key to applying the right amount in chemical reactions.

Calculations with Uncertainty

Performing calculations with measurements often involves working with uncertainties. It's essential to account for the range that uncertainties create to maintain the accuracy and reliability of your results. In our example with the 10-mL pipet, we determined that its volume range is from 9.99 mL to 10.01 mL due to an uncertainty of \(\pm 0.01\, \mathrm{mL}\).

When adding or subtracting measurements, you combine absolute uncertainties directly. For instance, with the nominal pipet value of 10.00 mL, subtract and add the uncertainty to get:

• Minimum value: \(10.00\, \mathrm{mL} - 0.01\, \mathrm{mL} = 9.99\, \mathrm{mL}\)
• Maximum value: \(10.00\, \mathrm{mL} + 0.01\, \mathrm{mL} = 10.01\, \mathrm{mL}\)

This method is applicable in any scientific context where measurement precision is pivotal. Integrating these calculations into your method helps verify:

• The reliability of collected data
• The accuracy of experimental methods

Understanding and executing calculations with uncertainty make theoretical and applied sciences more robust and trustworthy.