Problem 30 - Chemistry and Chemical Reactivity

Question

The accepted value of the melting point of pure aspirin is \(135^{\circ} \mathrm{C} .\) Trying to verify that value, you obtain the melting points of \(134^{\circ} \mathrm{C}, 136^{\circ} \mathrm{C}, 133^{\circ} \mathrm{C},\) and \(138^{\circ} \mathrm{C}\) in four separate trials. Your partner finds melting points of \(138^{\circ} \mathrm{C}, 137^{\circ} \mathrm{C}, 138^{\circ} \mathrm{C},\) and \(138^{\circ} \mathrm{C}\) (a) Calculate the average value and percent error for you and your partner. (b) Which of you is more precise? More accurate?

Step-by-Step Solution

Answer

Your averages are closer to the accepted value, making you more accurate, but your partner's measurements are more precise.

Step 1: Calculate Your Average Melting Point

To find your average melting point, add all of your measurements together and divide by the number of measurements. You have measurements of \(134^{\circ} \mathrm{C}, 136^{\circ} \mathrm{C}, 133^{\circ} \mathrm{C},\) and \(138^{\circ} \mathrm{C}\).\[\text{Your Average} = \frac{134 + 136 + 133 + 138}{4} = \frac{541}{4} = 135.25^{\circ} \mathrm{C}\]

Step 2: Calculate Partner's Average Melting Point

To find your partner's average melting point, add all of their measurements together and divide by the number of measurements. Your partner's measurements are \(138^{\circ} \mathrm{C}, 137^{\circ} \mathrm{C}, 138^{\circ} \mathrm{C},\) and \(138^{\circ} \mathrm{C}\).\[\text{Partner's Average} = \frac{138 + 137 + 138 + 138}{4} = \frac{551}{4} = 137.75^{\circ} \mathrm{C}\]

Step 3: Calculate Your Percent Error

Percent error is calculated using the formula:\[\text{Percent Error} = \frac{|\text{Accepted Value} - \text{Experimental Average}|}{\text{Accepted Value}} \times 100\%\]For your experiment:\[\text{Your Percent Error} = \frac{|135 - 135.25|}{135} \times 100\% \approx 0.185\%\]

Step 4: Calculate Partner's Percent Error

For your partner's experiment, use the same percent error formula:\[\text{Partner's Percent Error} = \frac{|135 - 137.75|}{135} \times 100\% \approx 2.037\%\]

Step 5: Determine Precision

Precision is about how close the measurements are to each other. You can consider the range or standard deviation of the values. Your range is \(138 - 133 = 5\) and your partner's range is \(138 - 137 = 1\). Since your partner has a smaller range, their measurements are more precise.

Step 6: Determine Accuracy

Accuracy is about how close the average measurement is to the accepted value. Yours is \(135.25^{\circ} \mathrm{C}\) with a percent error of about \(0.185\%\), closer to the actual \(135^{\circ} \mathrm{C}\) than your partner's \(137.75^{\circ} \mathrm{C}\) with a \(2.037\%\) error. Thus, you are more accurate.

Key Concepts

Percent Error Calculation

In experimental chemistry, calculating percent error is fundamental in assessing how close your experimental results are to the accepted or true values. It's a simple way to gauge accuracy and involves a few straightforward steps. First, you need the accepted value and the experimental average from your measurements. In the provided exercise, the accepted melting point of aspirin is given as 135°C.

The percent error formula is:

• Subtract the experimental average from the accepted value.
• Take the absolute value to avoid negative results.
• Divide this value by the accepted value.
• Finally, multiply by 100 to convert it into a percentage.

For example, if your average is 135.25°C, the percent error would be:\[\text{Percent Error} = \frac{|135 - 135.25|}{135} \times 100\% \approx 0.185\%\]A lower percent error indicates that your experimental values are very close to the true value, meaning high accuracy in your measurements.

Accuracy vs Precision

In the realm of experimental chemistry, it's crucial to understand the difference between accuracy and precision, as they reflect distinct aspects of measurement quality. **Accuracy** is about how close a measurement is to the true or accepted value while **precision** refers to the consistency of repeated measurements.

Let's break this down further:

• Accuracy tells us if our experimental results hit the target (the accepted value). If your average melting point of aspirin is 135.25°C and the accepted value is 135°C, your measurements are accurate as they're very close to the target.
• Precision is how close the measurements are to each other regardless of their proximity to the accepted value. It’s about consistency. If your partner repeatedly measures 138°C, the precision is high because these values are close together, even if they're not on target.

Determine both when analyzing data to understand the reliability and validity of experimental results.

Experimental Chemistry Methods

Understanding experimental methods in chemistry is essential for obtaining reliable and accurate data. These methods can range from simple temperature measurements to complex instrumental techniques, each designed to test and validate scientific hypotheses.

When determining melting points, different approaches and techniques can ensure accuracy and precision:

• **Proper Calibration**: Ensure all instruments, like thermometers, are properly calibrated for reliable readings.
• **Consistent Conditions**: Keeping conditions constant across trials minimizes variables that could skew results, such as pressure fluctuations or impurities.
• **Replicate Trials**: Conduct multiple trials and calculate an average to mitigate random errors and improve data quality.
• **Use of Standards**: Comparing results with known standards or controls can help correct discrepancies and increase confidence in the findings.

Adhering to these practices in experimental chemistry enables scientists to produce data that can be trusted for its validity and reliability, ultimately leading to more conclusive experimental outcomes.