Question

The accepted density for copper is 8.96 g/mL. Calculate the percent error for each of these measurements. \(\begin{array}{ll}{\text { a. } 8.86 \mathrm{g} / \mathrm{mL}} & {\text { c. } 9.00 \mathrm{g} / \mathrm{mL}} \\ {\text { b. } 8.92 \mathrm{g} / \mathrm{mL}} & {\text { d. } 8.98 \mathrm{g} / \mathrm{mL}}\end{array}\)

Short answer

The percent errors for the given measurements of the density of copper are: a. 1.12%, b. 0.45%, c. 0.45%, and d. 0.22%.

Step-by-step solution

Identify the values

We are given the accepted density of copper as 8.96 g/mL. For each of the given measurements (a, b, c, and d), we will find the percent error using the formula mentioned earlier.

Calculate the percent error for measurement a (8.86 g/mL)

From the given data, the experimental value (a) is 8.86 g/mL. Using the formula, we can calculate the percent error: \(Percent Error = \frac{|8.96 - 8.86|}{8.96} \times 100 \%\) \(Percent Error (a) = \frac{|0.10|}{8.96} \times 100 \% = 1.12 \%\) The percent error for measurement a is 1.12%.

Calculate the percent error for measurement b (8.92 g/mL)

From the given data, the experimental value (b) is 8.92 g/mL. Using the formula, we can calculate the percent error: \(Percent Error = \frac{|8.96 - 8.92|}{8.96} \times 100 \% \) \(Percent Error (b) = \frac{|0.04|}{8.96} \times 100 \% = 0.45 \% \) The percent error for measurement b is 0.45%.

Calculate the percent error for measurement c (9.00 g/mL)

From the given data, the experimental value (c) is 9.00 g/mL. Using the formula, we can calculate the percent error: \(Percent Error = \frac{|8.96 - 9.00|}{8.96} \times 100 \% \) \(Percent Error (c) = \frac{|-0.04|}{8.96} \times 100 \% = 0.45 \% \) The percent error for measurement c is 0.45%.

Calculate the percent error for measurement d (8.98 g/mL)

From the given data, the experimental value (d) is 8.98 g/mL. Using the formula, we can calculate the percent error: \(Percent Error = \frac{|8.96 - 8.98|}{8.96} \times 100 \% \) \(Percent Error (d) = \frac{|-0.02|}{8.96} \times 100 \% = 0.22 \% \) The percent error for measurement d is 0.22%.

Summary

We calculated the percent errors for each of the given measurements of the density of copper: a. 1.12% b. 0.45% c. 0.45% d. 0.22%

Key concepts

Density Measurement

Understanding density measurement is critical in fields like chemistry and physics. It is defined as the mass of a substance divided by its volume, commonly expressed in units like grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). When measuring density, precision is key, as it affects the reliability of experimental data and conclusions drawn from it. In chemistry, density can help identify substances, as each has a unique density. It is also essential for calculating other properties, such as purity or concentration.

Students should ensure they use calibrated equipment and correct formulas when determining density. Pay attention to the units used for mass and volume, as using different units can result in incorrect density values. For better understanding, compare measured densities to accepted standard values, as was done in the provided exercise with copper’s density.

Experimental Error

In chemistry, experimental error refers to the deviation of a measured value from the true value. It's an unavoidable part of scientific work and can arise from various sources, such as equipment limitations, observation mistakes, or environmental factors. Experimental error can be systematic, which affects all measurements in the same way, or random, which varies unpredictably.

Quantifying the experimental error helps assess the reliability of measurement and the overall experiment. The percent error is a popular way to express experimental error, calculated by dividing the absolute value of the difference between the experimental and accepted values by the accepted value, then multiplying by 100%. In the exercise about copper density, percent error calculations indicate the accuracy of each measurement. Understating experimental error allows students to improve their methodologies and recognize the limits of their results.

Chemistry Problem Solving

Effective chemistry problem solving involves a structured approach and critical thinking. Initially, identifying the known and unknown variables is essential, as it frames the problem. The next step usually requires selecting and applying the relevant chemical principles and formulas, much like using the percent error formula in our density measurement exercise.

It's important to focus on units and conversion factors during calculations to ensure accuracy. After solving the problem, it's beneficial to reflect on the result, considering if it makes sense within the context of the problem. Finally, cross-checking your work with peers or established data, as available, can validate the findings. In the classroom, hands-on experiments paired with problem-solving tasks enhance students’ understanding and application of theoretical knowledge.