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Chapter 1: Problem 77

The unit "troy ounce" is often used for precious metals such as gold (Au) and platinum ( \(\mathrm{Pt}\) ). ( 1 troy ounce \(=31.103\) g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? ( \(1 \mathrm{lb}=\) \(160 z ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

Short Answer

Expert verified
The gold coin weighs approximately 75 grams. A troy ounce is heavier than a conventional ounce.

Step by step solution

01

Convert Troy Ounces to Grams (part a)

Given that 1 troy ounce = 31.103 grams and we have a gold coin that weighs 2.41 troy ounces. The mass in grams can be calculated by multiplying the weight of the gold coin in troy ounces by the conversion factor. So, \(weigth_{grams} = 2.41 troy ounces * 31.103 \frac{g}{troy ounce}\)
02

Calculation of Weight in grams

When multiplying 2.41 troy ounces by 31.103, the 'troy ounces' units cancel out, and we're left with the weight in grams. Hence, \(weigth_{grams} = 2.41*31.103 = 74.9583g\).
03

Conversion of Ounces to Grams (part b)

We know that 1 lb = 16 oz = 453.6 g. So, 1 oz = 28.35 g (by dividing 453.6 by 16). This gives the conversion factor that we'll use to convert a troy ounce to a conventional ounce.
04

Comparison of Troy Ounces and Ounces

As calculated in step 1, a troy ounce is 31.103 grams. From step 3, we know that a conventional ounce is 28.35 grams. Thus, a troy ounce is heavier than a conventional ounce because it is 31.103 grams -- which is more than 28.35 grams.

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Most popular questions from this chapter

In determining the density of a rectangular metal bar, a student made the following measurements: length, \(8.53 \mathrm{~cm} ;\) width, \(2.4 \mathrm{~cm} ;\) height, \(1.0 \mathrm{~cm}\) mass, 52.7064 g. Calculate the density of the metal to the correct number of significant figures.

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