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Chapter 2: Problem 115

Four liquids have densities as follows: Liquid W: \(1.5\) \(\mathrm{g} / \mathrm{mL}\); Liquid X: \(12 \mathrm{~g} / \mathrm{mL}\); Liquid Y: \(0.8 \mathrm{~g} / \mathrm{mL}\); Liquid \(\mathrm{Z}\) : \(2.8 \mathrm{~g} / \mathrm{mL}\). When poured into a container, what is the correct arrangement of these liquids from the bottom of the container to the top? A. \(Y, W, Z, X\) B. \(X, Z, W, Y\) C. \(X, W, Z, Y\)

Short Answer

Expert verified
Option B: X, Z, W, Y

Step by step solution

01

- Identify Densities

List the given densities of each liquid: Liquid W: 1.5 g/mL Liquid X: 12 g/mL Liquid Y: 0.8 g/mL Liquid Z: 2.8 g/mL
02

- Understand Density and Layering

Recall that liquids layer based on their density when mixed. The densest liquid will settle at the bottom, and the least dense liquid will float to the top.
03

- Compare and Arrange the Densities

Arrange the densities from highest to lowest: Liquid X (12 g/mL), Liquid Z (2.8 g/mL), Liquid W (1.5 g/mL), Liquid Y (0.8 g/mL)
04

- Arrange the Liquids in the Container

Using the arranged densities, the order from bottom to top in the container will be: Liquid X at the bottom, followed by Liquid Z, then Liquid W, and finally Liquid Y at the top.
05

- Select the Correct Option

Based on the arrangement, the correct answer is the option that lists the liquids as X, Z, W, Y: B. X, Z, W, Y

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Density
Density is a core concept in understanding how different liquids behave when mixed together. It is defined as mass per unit volume and is typically measured in grams per milliliter (g/mL). The formula to calculate density is:
\( \rho = \frac{m}{V} \)
Where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume.
Liquids with higher densities are heavier for the same volume compared to those with lower densities. Therefore, when two liquids of different densities are poured into the same container, the denser liquid will sink below the less dense liquid.
In our exercise, we identified the densities of four liquids as follows:
  • Liquid W: 1.5 g/mL
  • Liquid X: 12 g/mL
  • Liquid Y: 0.8 g/mL
  • Liquid Z: 2.8 g/mL
Liquid Layering
Liquid layering is an interesting phenomenon where different liquids form distinct layers when combined in a single container. This happens due to the varying densities of the liquids. The rule is simple:
  • The liquid with the highest density settles at the bottom.
  • The liquid with the next highest density forms a layer above it.
  • This pattern continues until the liquid with the lowest density forms the top layer.
To find the correct arrangement, we first compare the densities:
Liquid X (12 g/mL), Liquid Z (2.8 g/mL), Liquid W (1.5 g/mL), Liquid Y (0.8 g/mL).
Based on this, Liquid X will be at the bottom, then Liquid Z above it, followed by Liquid W, and finally, Liquid Y will be on top. This translates into the correct arrangement from bottom to top as X, Z, W, and Y.
Science Problem-Solving
Science problem-solving often involves breaking down a problem into manageable steps and analyzing each step critically. Let's recap the steps employed in solving the exercise about liquid densities:
  1. Identify Densities: List the given densities of each liquid.
  2. Understand Density and Layering: Recall that denser liquids settle below less dense ones.
  3. Compare and Arrange the Densities: Arrange the densities from highest to lowest.
  4. Arrange the Liquids in the Container: Based on the arranged densities, assign the correct order from bottom to top.
  5. Select the Correct Option: Match the arranged order with the given options to select the correct one.
The methodical approach helps to avoid any confusion and ensures accurate results. In this case, the option B (X, Z, W, Y) matches our layered arrangement based on densities, proving it to be the correct answer.

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