Problem 27 - General Chemistry

Question

You need a thermometer that is accurate to \(\pm 5^{\circ} \mathrm{C}\) to conduct some experiments in the temperature range of \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). You find one in your lab drawer that has lost its markings. a. What experiments could you do to make sure your thermometer is suitable for your experiments? b. Assuming that the thermometer works, what procedure could you follow to put a scale on your thermometer that has the desired accuracy?

Step-by-Step Solution

Answer

Calibrate using freezing and boiling points, mark points, verify accuracy with known temperatures.

Step 1: Understand the Problem

You need a thermometer with an accuracy of \( \pm 5^{\circ} \mathrm{C} \). To determine if your unmarked thermometer is suitable, you need to establish reference points to calibrate it for the entire experimental range (\(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\)).

Step 2: Calibrating the Thermometer with Fixed Points

Use the freezing point and boiling point of water as fixed reference points, which are \(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) respectively. Submerge the thermometer in a mixture of ice and water to mark the freezing point, then in boiling water to mark the boiling point.

Step 3: Verifying Intermediate Points

Perform additional experiments at known temperatures (e.g., room temperature, or the melting point of another substance) to see if the thermometer readings at these points correspond correctly. This helps ensure that the thermometer can measure accurately throughout the entire range.

Step 4: Mark the Thermometer with a Scale

Once the endpoints (\(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\)) are marked and you have verified intermediate accuracy, divide the thermometer into equal divisions to represent each degree Celsius.

Step 5: Testing for Desired Accuracy

After marking, test the thermometer in a lab to ensure at any point it does not exceed \(\pm 5^{\circ} \mathrm{C}\) error. You can do this by using a reference thermometer with known accuracy for comparison.

Key Concepts

Temperature Accuracy

Temperature accuracy is crucial when conducting experiments that depend on precise measurements. This accuracy ensures that the recorded temperature reflects the true conditions of the experiment. For our task, the thermometer must be accurate within a range of \( \pm 5^{\circ} \mathrm{C} \).

Achieving such accuracy involves not only the calibration of the thermometer but also its continued validation during its use. One important step is comparing the thermometer readings against a known standard, such as a reference thermometer with established accuracy. This comparison helps detect any discrepancies.

The accuracy of a thermometer can be compromised by various factors, including user error, faulty calibration, and environmental influences like changes in pressure or humidity. Thus, handling and repeating the calibration process regularly is key.

• Regular checks with a reliable reference thermometer
• Understanding and minimizing external factors that can affect readings
• Consistent calibration strategy

These efforts ensure the thermometer remains suitable for precise scientific work.

Freezing Point

The freezing point of water is a fundamental constant used for calibrating thermometers. Defined as \(0^{\circ} \mathrm{C}\), this point is essential for marking the first reference point during calibration. To use this point effectively, submerge the thermometer in a mixture of ice and water.

The mixture should be at equilibrium, with a consistent combination of ice and liquid water. By waiting for the thermometer to stabilize in this environment, you can accurately mark the \(0^{\circ} \mathrm{C}\) point on your instrument.

• Use pure or distilled water to avoid impurities affecting the freezing point.
• Ensure a good ice-to-water ratio to maintain a steady temperature.
• Allow ample time for the thermometer to adjust and stabilize before marking.

The freezing point provides a reliable baseline for further calibration and is universally recognized, making it an ideal and universally accepted calibration point.

Boiling Point

There's more than meets the eye to calibrating a thermometer at water's boiling point. In pure conditions, the boiling point is \(100^{\circ} \mathrm{C}\) at sea level. This serves as a second reference point to ensure accuracy beyond just one fixed mark.

During calibration, immerse the thermometer in boiling water and wait for its temperature reading to stabilize. It's essential to account for altitude, as higher elevations can lower boiling temperature. This is due to decreased atmospheric pressure.

• Use purified or distilled water for an accurate reading, minimizing chemical impurities.
• Conduct the test at normal atmospheric pressure or correct for altitude differences.
• Verify stability in the boiling point reading prior to marking.

This careful approach ensures that you accurately establish the upper limit for thermometer calibration.

Experiment Design

Designing an experiment to calibrate a thermometer involves several thoughtful steps to ensure that the desired accuracy is attained. The objective is to not just mark the known fixed points but also test and confirm accuracy across the range.

Let's start by establishing clear procedures with detailed steps for measuring and marking the thermometer at both freezing and boiling points. Use these points to create a scale. You also need control tests at intermediate temperatures to check the linearity and reliability of your thermometer across its range. This ensures it performs well in actual usage scenarios.

• Define fixed points accurately, such as freezing and boiling water.
• Use intermediate temperatures to verify and adjust readings.
• Include controls with a reference thermometer for precise validation.

Considering and planning each step carefully ensures a robust design to confirm the accuracy essential for reliable experimental results.