Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 85

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Chapter 1, Problem 85

A 40-lb container of peat moss measures 14 * 20 * 30 in. A 40-lb container of topsoil has a volume of 1.9 gal. (b) How many bags of peat moss are needed to cover an area measuring 15.0 ft * 20.0 ft to a depth of 3.0 in.?

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Key Concepts

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

Volume Calculation

To determine how many bags of peat moss are needed, it's essential to calculate the volume of the area to be covered. The volume can be found using the formula: Volume = Area × Depth. In this case, the area is 15.0 ft × 20.0 ft, and the depth is converted from inches to feet for consistency.

Unit Conversion

Unit conversion is crucial in this problem as it involves different units of measurement. The volume of the topsoil is given in gallons, while the area and depth are in feet. Understanding how to convert between cubic feet and gallons will allow for accurate comparisons and calculations of the materials needed.

Density and Weight Relationships

The relationship between weight and volume is important for determining how many bags of peat moss are required. Knowing the weight of the peat moss (40 lbs) and its volume (calculated from its dimensions) allows for the determination of how many bags are necessary to achieve the desired coverage. This concept ties together the physical properties of the materials involved.

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Density Concepts

Related Practice

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?

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

Saline solution used in hospital contains 0.9% sodium chloride by mass. Calculate the number of grams of sodium chloride in 0.5 gal of saline solution if the solution has a density of 1.01 g/mL.

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Textbook Question

The total rate at which power is used by humans worldwide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is 680 W>m2 (assuming no clouds). The area of Earth's disc as seen from the Sun is 1.28 * 1014 m2. The surface area of Earth is approximately 197,000,000 square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can convert only 10% of the available sunlight into useful power

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Textbook Question

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50% gold is 12 carat. State the purity of the gold jewelry in carats.

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Textbook Question

Judge the following statements as true or false. If you believe a statement to be false, provide a corrected version. (a) Air and water are both elements.

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