Problem 121 - Chemistry Matter and Change

Question

Predict Four graduated cylinders each contain a different liquid: A, B, C, and D. Liquid A: mass \(=18.5\) g; volume \(=15.0 \mathrm{mL}\) Liquid B: mass \(=12.8\) g; volume \(=10.0 \mathrm{mL}\) Liquid C: mass \(=20.5\) g; volume \(=12.0 \mathrm{mL}\) Liquid D: mass \(=16.5 \mathrm{g} ;\) volume \(=8.0 \mathrm{mL}\) Examine the information given for each liquid, and predict the layering of the liquids if they were carefully poured into a larger graduated cylinder.

Step-by-Step Solution

Answer

The layering of the liquids in a graduated cylinder would be: Liquid D at the bottom, followed by Liquid C, Liquid B, and Liquid A at the top.

Step 1: Calculate the densities of the liquids.

Calculate the density of each liquid using the formula Density \(=\frac{Mass}{Volume}\). - For Liquid A: Density A \(=\frac{18.5 \ \mathrm{g}}{15.0\ \mathrm{mL}}=\frac{37}{30}\ \frac{\mathrm{g}}{\mathrm{mL}}\) - For Liquid B: Density B \(=\frac{12.8\ \mathrm{g}}{10.0\ \mathrm{mL}}=\frac{32}{25}\ \frac{\mathrm{g}}{\mathrm{mL}}\) - For Liquid C: Density C \(=\frac{20.5\ \mathrm{g}}{12.0\ \mathrm{mL}}=\frac{41}{24}\ \frac{\mathrm{g}}{\mathrm{mL}}\) - For Liquid D: Density D \(=\frac{16.5\ \mathrm{g}}{8.0\ \mathrm{mL}}=\frac{33}{16}\ \frac{\mathrm{g}}{\mathrm{mL}}\)

Step 2: Compare the densities of the liquids.

Now that we have the densities of the liquids, let's compare their values to find the layering order: Density A \(=\frac{37}{30}\ \frac{\mathrm{g}}{\mathrm{mL}}\approx1.23\ \frac{\mathrm{g}}{\mathrm{mL}}\) Density B \(=\frac{32}{25}\ \frac{\mathrm{g}}{\mathrm{mL}}\approx1.28\ \frac{\mathrm{g}}{\mathrm{mL}}\) Density C \(=\frac{41}{24}\ \frac{\mathrm{g}}{\mathrm{mL}}\approx1.71\ \frac{\mathrm{g}}{\mathrm{mL}}\) Density D \(=\frac{33}{16}\ \frac{\mathrm{g}}{\mathrm{mL}}\approx2.06\ \frac{\mathrm{g}}{\mathrm{mL}}\)

Step 3: Arrange the liquids according to their densities.

From the comparison in Step 2, we can see that Liquid D has the highest density, followed by Liquid C, Liquid B, and Liquid A. Therefore, the layering of the liquids would be as follows: 1. Bottom layer: Liquid D 2. Second layer: Liquid C 3. Third layer: Liquid B 4. Top layer: Liquid A So, the layering of the four liquids, if they were carefully poured into a larger graduated cylinder, would be Liquid D at the bottom, followed by Liquid C, Liquid B, and Liquid A at the top.

Key Concepts

Liquid Layering

Liquid layering occurs when different liquids settle based on their densities after being mixed. This is because each liquid has a different mass per unit volume. If you gently pour one liquid over another, they will form layers if they don't mix. The denser liquid will move to the bottom, while the less dense ones float above.
This principle is often used in kitchen science experiments and helps in understanding how oil might float on water. For instance, in this exercise, by calculating the densities of liquids A, B, C, and D, you can predict how they stack up when poured together.
Given their densities, Liquid D will form the bottom layer, as it is the heaviest per unit volume, and Liquid A will remain the topmost due to its lighter density.

Graduated Cylinder

A graduated cylinder is a common laboratory tool used to measure the volume of a liquid. It is cylindrical and marked with lines (graduations) to indicate volume levels. Graduated cylinders come in various sizes, typically ranging from 10 mL to a few liters.
They are specifically designed to provide precision in volume measurements. This is crucial when you need to correctly calculate the density of a liquid, which relies on accurate volume measurements. For effective use, it's important to read the liquid level at eye level and record the volume at the bottom of the meniscus, the curve seen at the liquid's surface.
In this exercise, graduated cylinders are essential for measuring the volume of liquids A, B, C, and D to proceed with density calculations.

Mass and Volume Calculation

To find the density of a liquid, you first need to measure its mass and volume. Mass is usually measured in grams using a balance scale. Volume, as mentioned, is measured using a graduated cylinder.
Once you have these two pieces of information, you can apply the density formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] By dividing the mass by the volume, you get a value that expresses how dense the liquid is. For example, if a liquid has a mass of 20 grams and a volume of 10 mL, its density would be 2 g/mL.
This calculation is the initial step in determining how liquids will layer when combined. In this case, calculating the density for each liquid A, B, C, and D allowed the prediction of their layering order.

Density Comparison

Density comparison is essential for predicting how different liquids will behave in a mixture. By comparing the densities, you can anticipate which liquid will float and which will sink. Each liquid has its specific density, calculated using the formula discussed earlier.
In general, the liquid with the highest density will sink to the bottom, creating the densest layer, while the one with the lowest density stays at the top. By arranging the liquids from highest to lowest density, you can visually represent how they will organize themselves when mixed.
For this exercise, after comparing the calculated densities, Liquid D was found to have the highest density, placing it at the very bottom, followed by Liquid C, B, and A, respectively, in decreasing order of density. This sequence outcomes from their distinct mass and volume proportions.