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Ch.1 - Introduction: Matter, Energy, and Measurement
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 14th EditionCh.1 - Introduction: Matter, Energy, and Measurement문제 63
1장, 문제 63

Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 30 m x 25 m ceiling with gold leaf that is twelve-millionths of a centimeter thick. The density of gold is 19.32 g/cm3, and gold costs \$1654 per troy ounce (1 troy ounce = 31.1034768 g). How much will it cost the architect to buy the necessary gold?

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Calculate the volume of gold needed by multiplying the area of the ceiling by the thickness of the gold leaf. Use the formula: \( \text{Volume} = \text{Area} \times \text{Thickness} \).
Convert the volume from cubic centimeters to cubic meters, if necessary, to match the units of the area and thickness.
Use the density of gold to find the mass of gold required. Use the formula: \( \text{Mass} = \text{Density} \times \text{Volume} \).
Convert the mass of gold from grams to troy ounces using the conversion factor: 1 troy ounce = 31.1034768 g.
Calculate the cost by multiplying the number of troy ounces by the cost per troy ounce (\$1654).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume and Thickness Calculation

To determine the amount of gold needed, one must calculate the volume of gold leaf required to cover the ceiling. This involves multiplying the area of the ceiling (30 m x 25 m) by the thickness of the gold leaf, converted into centimeters. Understanding how to manipulate units and perform volume calculations is essential for solving the problem.
추천 영상:
가이드 코스
02:35
Constant-Volume Calorimetry

Density and Mass Relationship

Density is defined as mass per unit volume, and it plays a crucial role in converting the calculated volume of gold leaf into mass. The density of gold (19.32 g/cm³) allows us to find the mass by multiplying the volume by the density. This relationship is fundamental in determining how much gold is needed in grams before converting it to troy ounces for cost calculation.
추천 영상:
가이드 코스
01:56
Density Concepts

Cost Calculation and Unit Conversion

Once the mass of gold is determined, the next step is to calculate the cost based on the price per troy ounce. This requires converting grams to troy ounces using the conversion factor (1 troy ounce = 31.1034768 g). Understanding how to perform these conversions and apply the cost per unit is essential for arriving at the final cost for the architect.
추천 영상:
가이드 코스
02:12
Conversion Factors Example
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교과서 질문

Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: (a) a leaf (b) a 999 gold bar

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Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: (c) stainless steel.

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The density of air at ordinary atmospheric pressure and 25 C is 1.19 g/L. What is the mass, in kilograms, of the air in a room that measures 4.5 m * 5.0 m * 2.5 m?
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