(a) After the label fell off a bottle containing a clear...

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A $25.0-\mathrm{mL}$ portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at $15^{\circ} \mathrm{C}$ as $0.8787 \mathrm{~g} / \mathrm{mL}$. Is the calculated density in agreement with the tabulated value? (b) An experiment requires $15.0 \mathrm{~g}$ of cyclohexane, whose density at $25^{\circ} \mathrm{C}$ is $0.7781 \mathrm{~g} / \mathrm{mL}$. What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of $5.0 \mathrm{~cm}$. What is the mass of the sphere if lead has a density of $11.34 \mathrm{~g} / \mathrm{cm}^{3} ?$ (The volume of a sphere is $(4 / 3) \pi r^{3},$ where $r$ is the radius.)

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A $25.0-\mathrm{mL}$ portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at $15^{\circ} \mathrm{C}$ as $0.8787 \mathrm{~g} / \mathrm{mL}$. Is the calculated density in agreement with the tabulated value? (b) An experiment requires $15.0 \mathrm{~g}$ of cyclohexane, whose density at $25^{\circ} \mathrm{C}$ is $0.7781 \mathrm{~g} / \mathrm{mL}$. What volume of cyclohexane should be used?
(c) A spherical ball of lead has a diameter of $5.0 \mathrm{~cm}$. What is the mass of the sphere if lead has a density of $11.34 \mathrm{~g} / \mathrm{cm}^{3} ?$ (The volume of a sphere is $(4 / 3) \pi r^{3},$ where $r$ is the radius.)

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Key Concepts

Volume Calculation

Volume calculation is the process of determining the amount of space that an object occupies. In chemical contexts, accurate volume measurements are crucial for converting quantities between mass and volume, especially when working with liquids of known density.

Spherical Volume Formula

The spherical volume formula, V = (4/3)?r³, is used to compute the volume of a sphere from its radius. This geometric formula is essential in physics and chemistry when calculating the mass of spherical objects from their volume and density.

Density

Density is a physical property that relates the mass of a substance to its volume, calculated by dividing mass by volume. It is used to characterize materials and compare measured values to known, standardized values, which is essential in verifying the identity of substances.

Mass-Volume Relationship

The mass-volume relationship is expressed through the density formula (density = mass/volume), which allows one to determine the volume of a substance given its mass (or vice versa) when the density is known. This is particularly important in laboratory measurements and chemical experiments.

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