Textbook Question
(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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Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 38c
(c) A spherical ball of lead has a diameter of 5.0 cm. What is the mass of the sphere if lead has a density of 11.34 g>cm3? (The volume of a sphere is 14>32pr3, where r is the radius.)
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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 mass per unit volume and is a key property of materials. It is typically expressed in grams per cubic centimeter (g/cm³) for solids and liquids. In this problem, the density of lead is given as 11.34 g/cm³, which will be used to calculate the mass of the lead sphere once its volume is determined.
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01:56
Density Concepts
Volume of a Sphere
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. The radius is half of the diameter, so for a sphere with a diameter of 5.0 cm, the radius would be 2.5 cm. This volume will be essential for finding the mass of the lead sphere using its density.
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02:35Constant-Volume Calorimetry
Mass Calculation
Mass can be calculated using the formula mass = density × volume. Once the volume of the sphere is calculated using the radius, and knowing the density of lead, this formula allows us to find the mass of the lead sphere. This relationship is fundamental in chemistry for converting between different properties of substances.
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03:12Molar Mass Calculation Example
Related Practice
Textbook Question
(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-mL portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at 15 °C as 0.8787 g/mL. Is the calculated density in agreement with the tabulated value?
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Textbook Question
(b) An experiment requires 15.0 g of cyclohexane, whose density at 25 C is 0.7781 g>mL. What volume of cyclohexane should be used?
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Textbook Question
If on a certain year, an estimated amount of 4 million metric
tons (1 metric ton = 1000 kg) of nitrous oxide 1N2O2 was
emitted worldwide due to agricultural activities, express this
mass of N2O in grams without exponential notation, using
an appropriate metric prefix.
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Textbook Question
Use of the British thermal unit (Btu) is common in some types of engineering work. A Btu is the amount of heat required to raise the temperature of 1 lb of water by 1°F. Calculate the number of joules in a Btu.
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Textbook Question
A watt is a measure of power (the rate of energy change) equal to 1 J/s. (b) An adult person radiates heat to the surroundings at about the same rate as a 100-watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?
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