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Ch.1 - Introduction: Matter, Energy, and Measurement
All textbooksBrown 15th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblem 39d
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Chapter 1, Problem 39d

(d) A cubic piece of metal measures 5.00 cm on each edge. If the metal is nickel, whose density is 8.90 g/cm3, what is the mass of the cube?

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<Calculate the volume of the cube using the formula for the volume of a cube: \( V = \text{side}^3 \). Here, the side length is 5.00 cm.>
<Substitute the side length into the volume formula: \( V = (5.00 \text{ cm})^3 \).>
<Calculate the volume in cubic centimeters.>
<Use the density formula to find the mass: \( \text{mass} = \text{density} \times \text{volume} \).>
<Substitute the known values into the density formula: \( \text{mass} = 8.90 \text{ g/cm}^3 \times \text{volume} \).>

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as the mass of an object divided by its volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps identify substances and can be used to calculate mass or volume when the other is known. In this case, the density of nickel is given as 8.90 g/cm³, which will be used to find the mass of the cube.
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Volume of a Cube

The volume of a cube is calculated using the formula V = a³, where 'a' is the length of one edge of the cube. For a cube measuring 5.00 cm on each edge, the volume can be determined by cubing the edge length. This volume will be essential for calculating the mass of the nickel cube using its density.
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Mass Calculation

Mass can be calculated using the formula: mass = density × volume. Once the volume of the cube is determined, multiplying it by the density of nickel will yield the mass of the cube. This relationship is fundamental in chemistry for converting between mass, volume, and density.
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Textbook Question

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a 45-mL sample of the substance. She then measured the mass of the sample, finding that it weighed 38.5 g. She knew that the substance had to be either isopropyl alcohol 1density 0.785 g/mL2 or toluene (density 0.866 g/mL). What are the calculated density and the probable identity of the substance?

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Textbook Question

b. An experiment requires 78.1 g of benzene, a liquid whose density is 0.876 g/mL. Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use?

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Textbook Question

c. A cubic piece of metal measures 5.00 cm on each edge. If the metal is nickel, whose density is 8.90 g/cm3, what is the mass of the cube?

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Textbook Question

a. After the label fell off a bottle containing a clear liquid believed to be a solvent called tetrahydrofuran, a chemist measured the density of the liquid to verify its identity. A 25.0-mL portion of the liquid had a mass of 22.08 g. A chemistry handbook lists the density of tetrahydrofuran at 25 °C as 0.8833 g/mL. Is the calculated density in agreement with the tabulated value?

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Textbook Question

b. An experiment requires 50.0 g of a substance called n-hexane, whose density at 25 °C is 0.6606 g/mL. What volume of n-hexane should be used?

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Textbook Question

The density of titanium metal is 4.506 g/cm3 at 20 °C. What is the mass of a spherical ball of titanium with a diameter of 2.00 cm. [The volume of a sphere is (4/3) πr3, where r is the radius.]

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