Question

density study guide
density = \frac{mass}{volume}
teks 6.6b calculate density of an unknown substance.

1. if each of the liquids in the container has the same volume, what can be said about the liquids?

a. liquid a has a greater mass than b and c.
b. liquid c has the greatest mass.
c. the liquids are the same substance.

1. which liquid has the greatest density? ______
2. which liquid has the least density? ______

(image: cylinder with liquids a (top), b (middle), c (bottom))

Explanation:

Question 1

Step1: Recall density formula

The density formula is $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$. Given that the volume of each liquid is the same (same container volume).

Step2: Analyze mass - density relationship

From $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$, when volume ($V$) is constant, density ($
ho$) is directly proportional to mass ($m$), i.e., $
ho\propto m$ (since $V$ is constant, $
ho = \frac{m}{V}\implies m=
ho V$). The liquid at the bottom (C) is more dense (as denser liquids sink), so it has more mass. Liquid A is at the top, so it has the least mass. So if volume is same, mass of A < B < C. So option C says "The liquids are the same substance" which is wrong (different densities as they are in different layers). Option A: "Liquid A has a greater mass than B and C" is wrong (A has least mass). Option B: "Liquid C has the greatest mass" is correct as $m =
ho V$ and $
ho_C>
ho_B>
ho_A$ (from layering) and $V$ same, so $m_C > m_B>m_A$.

Step1: Recall density and layering

In a mixture of liquids, the denser liquid sinks to the bottom and the less dense liquid floats on top. So the liquid at the bottom has the highest density and the liquid at the top has the lowest density.

Step2: Identify the bottom - most liquid

From the diagram, Liquid C is at the bottom, then B, then A (A is at the top). So the liquid at the bottom (C) has the greatest density.

Step1: Recall density and layering

In a mixture of liquids, the denser liquid sinks to the bottom and the less dense liquid floats on top. So the liquid at the top has the least density.

Step2: Identify the top - most liquid

From the diagram, Liquid A is at the top, then B, then C (C is at the bottom). So the liquid at the top (A) has the least density.

Answer:

B. Liquid C has the greatest mass.

Question 2