Question

These organic solvents are used to clean compact discs: $$\begin{array}{lc}\text { Solvent } & \text { Density }(\mathrm{g} / \mathrm{mL}) \text { at } 20^{\circ} \mathrm{C} \\\\\hline \text { Chloroform } & 1.492 \\\\\text { Diethyl ether } & 0.714 \\\\\text { Ethanol } & 0.789 \\\\\text { Isopropanol } & 0.785 \\\\\text { Toluene } & 0.867\end{array}$$ (a) If a 15.00-mL sample of CD cleaner weighs \(11.775 \mathrm{~g}\) at \(20^{\circ} \mathrm{C}\). which solvent does the sample most likely contain? (b) The chemist analyzing the cleaner calibrates her equipment and finds that the pipet is accurate to \(\pm 0.02 \mathrm{~mL},\) and the balance is accurate to \(\pm 0.003 \mathrm{~g}\). Is this equipment precise enough to distinguish between ethanol and isopropanol?

Short answer

a) Isopropanol. b) No, the equipment is not precise enough to distinguish between ethanol and isopropanol.

Step-by-step solution

Find the density of the CD cleaner sample

First, use the formula for density: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). The mass of the CD cleaner is given as 11.775 g and the volume is 15.00 mL. Thus, the density \(\rho\) is calculated as: \ \[ \rho = \frac{11.775 \text{ g}}{15.00 \text{ mL}} = 0.785 \text{ g/mL} \]

Compare to the table

Compare the calculated density to the densities of the given solvents: Chloroform (1.492 g/mL), Diethyl ether (0.714 g/mL), Ethanol (0.789 g/mL), Isopropanol (0.785 g/mL), and Toluene (0.867 g/mL). The calculated density (0.785 g/mL) matches closely with the density of isopropanol (0.785 g/mL).

Determine precision of equipment

The equipment's accuracy is given as ±0.02 mL for volume and ±0.003 g for mass. To determine if the equipment is precise enough to distinguish between ethanol and isopropanol, calculate the possible density ranges considering the measurement errors for both solvents. For ethanol (0.789 g/mL): \ \[ \text{density range} = \frac{11.775 \pm 0.003 \text{ g}}{15.00 \pm 0.02 \text{ mL}} \] For isopropanol (0.785 g/mL): \ \[ \text{density range} = \frac{11.775 \pm 0.003 \text{ g}}{15.00 \pm 0.02 \text{ mL}} \] The possible densities considering errors are very close, thus it is difficult to distinguish between ethanol and isopropanol with the given precision.

Key concepts

density calculation

Density is a fundamental concept in chemistry, calculated as the mass divided by the volume of a substance. For the given exercise, the mass is 11.775 g and the volume is 15.00 mL. Using the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), we find the density to be \( \rho = \frac{11.775 \text{ g}}{15.00 \text{ mL}} = 0.785 \text{ g/mL} \).
This calculated density is then compared to the densities of other solvents. This step helps identify which solvent is most likely present based on similar densities. Always remember to use the correct units and perform calculations with precision to ensure accuracy.

organic solvents

Organic solvents are used in various industries for cleaning and dissolving substances. In this exercise, solvents like Chloroform, Diethyl ether, Ethanol, Isopropanol, and Toluene are mentioned. They each have unique densities and boiling points, making them suitable for different cleaning tasks.
To identify the solvent used in the CD cleaner, it's essential to understand the properties of each solvent. For instance, Chloroform has a high density of 1.492 g/mL, making it much heavier than solvents like Diethyl ether (0.714 g/mL) or Isopropanol (0.785 g/mL). These differences help determine the suitability and safety of use, considering their chemical properties and how they interact with different materials.
The calculated density helps chemists infer which solvent is present by comparing it with known values. Understanding these properties ensures safer and more effective use of organic solvents in various applications.

precision of measurement

Precision in measurement is crucial in chemical analysis. It ensures results are reliable and can be replicated. In the exercise, the chemist's equipment has an accuracy given as ±0.02 mL for volume and ±0.003 g for mass. This means any measurement taken can differ by these amounts.
For instance, if a volume measurement is 15.00 mL, the actual volume could be between 14.98 mL and 15.02 mL. Similarly, for a mass measurement of 11.775 g, the actual mass could range from 11.772 g to 11.778 g.
These small tolerances are vital when distinguishing between substances with similar densities. The slight difference in density values between ethanol (0.789 g/mL) and isopropanol (0.785 g/mL) may be hard to detect due to these measurement errors. Always consider the precision limits of your equipment during experiments to understand the reliability of your results.

chemical analysis methods

Chemical analysis involves various methods to determine the composition and properties of substances. In this exercise, the method used is density measurement, a fundamental property that can identify and differentiate between substances.
Other common methods in chemical analysis include chromatography, spectroscopy, and titration. Each method offers different advantages and is suited for specific analytical needs. For instance, chromatography separates compounds based on their movement through a medium, while spectroscopy analyzes the interaction between matter and electromagnetic radiation.
Choosing the correct analytical method depends on factors like the nature of the sample, the property being measured, and the required precision and accuracy. In our case, density measurement offers a straightforward approach to identify the solvent, provided the equipment's precision is high.

laboratory equipment accuracy

The accuracy of laboratory equipment is vital for precise and reliable measurements. Accuracy refers to how close a measurement is to the true value. In this exercise, the pipet and balance used have specific accuracy levels: ±0.02 mL for the pipet and ±0.003 g for the balance.
These accuracy details help assess the reliability of the results. When measuring a solvent's density, even small inaccuracies can lead to incorrect identifications if the density values of possible solvents are close.
Regular calibration of equipment is essential to maintain accuracy. This involves comparing the measurements from the device against known standards and adjusting the device as necessary. Proper maintenance and understanding of your equipment's limits ensure the highest quality in chemical analysis. Always report the accuracy limits of your measurements to provide context to your results.