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Chapter 2: Problem 209

Without doing any numerical calculations, determine which would have the smallest volume: (a) \(50 \mathrm{~g}\) of water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ) (b) \(50 \mathrm{~g}\) of salt water (density \(=2.3 \mathrm{~g} / \mathrm{mL}\) ) (c) \(50 \mathrm{~g}\) of mercury (density \(=13.6 \mathrm{~g} / \mathrm{mL}\) ) (d) \(50 \mathrm{~g}\) of alcohol (density \(=0.89 \mathrm{~g} / \mathrm{mL}\) ) Explain your reasoning.

Short Answer

Expert verified
Out of the given substances, 50 grams of mercury will have the smallest volume as it has the highest density (13.6 g/mL).

Step by step solution

01

Identify the densities

First, let's identify the densities of the given substances. Water has a density of 1.0 g/mL, saltwater has a density of 2.3 g/mL, mercury has a density of 13.6 g/mL, and alcohol has a density of 0.89 g/mL.
02

Compare the densities

We need to compare the densities of the substances. If we look at the densities given, we can identify that mercury has the highest density (13.6 g/mL), followed by saltwater (2.3 g/mL), water (1.0 g/mL), and finally alcohol (0.89 g/mL).
03

Determine smallest volume

As we established earlier, the substance with the smallest volume for 50 grams will have the highest density. This is because volume is inversely proportional to density (i.e., volume = mass/density). Since mercury has the highest density, it will have the smallest volume for the same mass.
04

Unveil the answer

Therefore, out of the given substances, 50 grams of mercury will have the smallest volume.

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