Problem 101 - Chemistry Matter and Change

Question

Students used a balance and a graduated cylinder to collect the data shown in Table \(2.6 .\) Calculate the density of the sample. If the accepted density of this sample is 6.95 \(\mathrm{g} / \mathrm{mL}\) , calculate the percent error. \(\begin{array}{ll}{\text { Mass of sample }} & {20.46 \mathrm{g}} \\ {\text { Volume of water }} & {40.0 \mathrm{mL}} \\ {\text { Volume of water }+\text { sample }} & {43.0 \mathrm{mL}}\end{array}\)

Step-by-Step Solution

Answer

The volume of the sample is 3.0 mL (43.0 mL - 40.0 mL). The density of the sample is \( \frac{20.46 \text{ g}}{3.0 \text{ mL}} = 6.82 \frac{\text{g}}{\text{mL}} \). The percent error is \( \left| \frac{6.82 - 6.95}{6.95} \right| \times 100 \approx 1.87 \% \).

Step 1: Calculate the volume of the sample

To find the volume of the sample, we need to subtract the initial volume of water from the volume of water plus the sample. The given data are: - Volume of water: 40 mL - Volume of water + sample: 43 mL So, the volume of the sample would be: Volume of the sample = (Volume of water + sample) - Volume of water

Step 2: Calculate the density of the sample

Now that we have the volume of the sample, we can calculate its density. The formula for density is: Density = Mass / Volume The given mass of the sample is 20.46 g. We will now plug in the mass and volume values into the formula to find the density.

Step 3: Calculate the percent error

To calculate the percent error, we will compare the experimental density with the accepted density (6.95 g/mL) using the following formula: Percent Error = \( \left| \frac{Experimental Density - Accepted Density}{Accepted Density} \right| \) × 100 Now, let's plug in the values and calculate the percent error.

Step 4: Summary

1. Calculate the volume of the sample by subtracting the initial volume of water from the volume of water plus the sample. 2. Calculate the density of the sample using the formula Density = Mass / Volume. 3. Calculate the percent error by comparing the experimental density to the accepted density using the Percent Error formula.

Key Concepts

Density Formula

When students encounter the concept of density in chemistry, it's important to provide a clear and comprehensible explanation. Density, fundamentally, serves as a measure of how much mass is contained in a given volume. The density formula, which is a cornerstone of understanding chemical measurements, is quite straightforward:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
By using this formula, it becomes possible to compare different substances based on their mass-to-volume ratios. In practical terms, when students performed the experiment as depicted in the exercise, they had to calculate the density of a sample. They first determined the volume of the sample by measuring the water displacement and then applied the formula with the given mass of the sample. This simple equation is not just theoretical—it's a hands-on tool for the practical identification and characterization of substances in a lab setting.

Percent Error Calculation

Understanding percent error calculation is essential for students in assessing the accuracy of their experiments in chemistry. The percent error reveals how much an experimental value deviates from a known or accepted value and is expressed as a percentage. The formula for percent error is:

\[ \text{Percent Error} = \left| \frac{\text{Experimental Value} - \text{Accepted Value}}{\text{Accepted Value}} \right| \times 100 \% \]
This calculation provides a standardized way to measure the precision of experimental results. For the implemented exercise, students would use the density they calculated from their experiment as the experimental value and compare it with the accepted density of the sample. The percent error thus gives insight into the reliability of the measurement techniques and equipment used, such as the balance and graduated cylinder. Reflecting on the percent error can also lead to improving experimental procedures in future trials.

Chemical Measurement

In the realm of chemistry, precise measurement is the foundation of reliable data and successful experiments. Chemical measurement involves various methods and tools to determine quantities related to chemical processes or properties, such as mass, volume, concentration, and, as previously discussed, density. When students conducted their experiment, it was imperative for them to use a balance to measure the mass of the sample and a graduated cylinder to measure the volume of water displaced by the sample— each representing a chemical measurement. These basic tools are essential for obtaining accurate readings that feed into calculations like density and percent error.

It's imperative for learners to understand not only how to perform these measurements but also how to read and interpret the data collected. Mastery in chemical measurement not only builds a student's proficiency in conducting experiments but also their confidence in the precision of their work.