Question

problem - solving lab 6.2
use numbers
why does ice float? most liquids contract when frozen. water is different; it expands. the density of water changes when ice forms, allowing ice to float. density refers to compactness and is often described as the mass of a substance per unit of volume. a mathematical expression of density would read as follows:
density = \\( \frac { \text { mass } } { \text { volume } } \\)
solve the problem
examine the following table. it shows the volume and mass for a sample of water and ice.
thinking critically

1. compare how does the density of ice compare with the density of water? use specific values and proper units expressing density in your answer. which of the two, ice or water, is less compact? explain your answer.
2. think critically are the molecules of water moving closer together or farther apart as water freezes? explain.
3. infer explain why a glass bottle filled with water might shatter if placed in a freezer.
4. recognize cause and effect explain why ice forming within a living organism may result in its death.

Explanation:

Step1: Calculate density of water

Using the formula \(Density=\frac{Mass}{Volume}\), for water: \(Density_{water}=\frac{126\ g}{126\ cm^{3}} = 1\ g/cm^{3}\)

Step2: Calculate density of ice

For ice: \(Density_{ice}=\frac{126\ g}{140\ cm^{3}}=\frac{9}{10}= 0.9\ g/cm^{3}\)

Step3: Compare densities

Since \(0.9\ g/cm^{3}<1\ g/cm^{3}\), ice is less dense. Less - dense substances are less compact.

Step4: Analyze molecular movement

As water freezes (to ice), since \(V_{ice}>V_{water}\) (for same mass) and \(Density=\frac{Mass}{Volume}\), the volume increases. So, molecules move farther apart.

Step5: Explain bottle - shattering

When water in the bottle freezes, it expands (as seen from volume change in data). The expansion exerts pressure on the glass bottle, causing it to shatter.

Step6: Explain organism - death

Ice formation in a living organism. Ice (less dense) has larger volume. The expansion of ice within cells (due to water freezing) can rupture cell membranes, leading to cell damage and organism death.

Answer:

1. The density of water is \(1\ g/cm^{3}\) (\(Density_{water}=\frac{126\ g}{126\ cm^{3}}\)) and the density of ice is \(0.9\ g/cm^{3}\) (\(Density_{ice}=\frac{126\ g}{140\ cm^{3}}\)). Ice is less dense (\(0.9<1\)) and thus less compact (since density is mass per unit volume, lower density means less mass per unit volume, i.e., less compact).
2. Molecules of water move farther apart as water freezes. Because, for the same mass (\(m = 126\ g\)), \(V_{ice}(140\ cm^{3})>V_{water}(126\ cm^{3})\). An increase in volume for the same number of molecules means molecules are farther apart.
3. When water in the bottle freezes, it expands (as \(V_{ice}>V_{water}\) for the same mass). The expansion of water (as it freezes to ice) exerts a large force on the glass bottle. Since glass is brittle, the bottle shatters.
4. Ice has a larger volume than the water it is formed from (for the same mass). When ice forms within a living organism, the expansion of ice can rupture cell membranes. Cell membrane rupture leads to loss of cell function, and if enough cells are damaged, the organism may die.