Open Question
By using estimation techniques, determine which of the following is the heaviest and which is the lightest: a 10-lb bag of fertilizer, a 10-kg bag of rice, or 2 gal of olive oil (density = 0.918 g/cm³).
Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 86
Water has a density of 0.997 g/cm3 at 25 °C; ice has a density of 0.917 g/cm3 at -10 °C. (a) If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 °C, what volume does the ice occupy? (b) Can the ice be contained within the bottle?
Verified step by step guidance1
Convert the volume of the water from liters to cubic centimeters (cm^3) using the conversion factor: 1 L = 1000 cm^3.
Calculate the mass of the water using the density of water at 25 °C: mass = density × volume.
Determine the volume of the ice using the mass of the water and the density of ice at -10 °C: volume of ice = mass / density of ice.
Compare the volume of the ice to the original volume of the bottle to determine if the ice can be contained within the bottle.
Discuss the implications of the volume change when water freezes and how it affects the containment within the bottle.
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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 critical property of substances. It is calculated using the formula density = mass/volume. In this question, the densities of water and ice are provided, which are essential for determining how the volume changes when water freezes. Understanding density helps explain why ice floats on water, as it is less dense than liquid water.
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Density Concepts
Volume and Volume Displacement
Volume refers to the amount of space an object occupies, measured in liters or cubic centimeters. When a substance changes state, such as water freezing into ice, its volume can change due to differences in density. The concept of volume displacement is important here, as the volume of ice formed from the water will determine whether it can fit back into the original container after freezing.
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Phase Changes
Phase changes refer to the transitions between solid, liquid, and gas states of matter. When water freezes, it undergoes a phase change from liquid to solid, which involves energy transfer and changes in molecular arrangement. Understanding phase changes is crucial for predicting how the properties of substances, such as volume and density, will alter during the freezing process.
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Related Practice
Open Question
Hexane 1density = 0.659 g/mL2 and acetic acid 1density = 1.0446 g/mL2 do not form a solution when mixed but separate into distinct layers. A piece of oak wood 1density = 900 kg/m32 is placed inside a test tube containing hexane and acetic acid; sketch how the three substances would position themselves.
Textbook Question
Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?
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Open Question
The mass of an empty oil drum is listed as 2.0×104 g. After a quantity of biodiesel fuel is added to the drum, the total mass is 7.05×105 g.
a. To how many significant figures should the mass of the biodiesel in the drum be reported?
b. The density of the biodiesel fuel is 0.875 g/cm3. What is the volume of biodiesel that has been added to the drum, in L?
Textbook Question
A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?
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Textbook Question
Automobile batteries contain sulfuric acid, which is commonly referred to as “battery acid.” Calculate the number of grams of sulfuric acid in 1.00 gal of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass.
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