(a) A sample of carbon tetrachloride, a liquid once used in...

(a) A sample of carbon tetrachloride, a liquid once used in dry cleaning, has a mass of $39.73 \mathrm{~g}$ and a volume of $25.0 \mathrm{mLat} 25^{\circ} \mathrm{C}$. What is its density at this temperature? Will carbon tetrachloride float on water? (Materials that are less dense than water will float.) (b) The density of platinum is $21.45 \mathrm{~g} / \mathrm{cm}^{3}$ at $20^{\circ} \mathrm{C}$. Calculate the mass of $75.00 \mathrm{~cm}^{3}$ of platinum at this temperature. (c) The density of magnesium is $1.738 \mathrm{~g} / \mathrm{cm}^{3}$ at $20^{\circ} \mathrm{C}$. What is the volume of $87.50 \mathrm{~g}$ of this metal at this temperature?

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Key Concepts

Density

Density is a physical property defined as mass divided by volume. It is used to characterize how much mass is contained in a given volume of a substance and is typically expressed in units such as g/mL or g/cm³. Understanding density is crucial when determining whether substances will behave differently in various environments or when calculating one variable if the other two are known.

Buoyancy

Buoyancy refers to the ability of an object to float in a fluid and is directly related to the object's density relative to that of the surrounding fluid. If the density of an object is less than that of the fluid in which it is submerged, it will float; if it is greater, it will sink. This concept is essential for predicting whether substances will float on water or other liquids.

Mass-Volume-Density Relationship

The mass-volume-density relationship is fundamental in solving problems where any two of these quantities are known and the third is unknown. The relationships are given by the formulas density = mass/volume, mass = density × volume, and volume = mass/density. This framework allows for the systematic conversion and calculation between these physical quantities in various contexts.

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