Chapter 1, Problem 1.77QP

The unit “troy ounce” is often used for precious metals such as gold (Au) and platinum (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? (11b = 16 oz; 11b = 453.⁶ g.)

Interpretation Introduction

Interpretation:

From the given data’s, it should be calculated the mass of gold coinin grams and it should be checked whether a troy ounce is heavier or lighter than an ounce.

Concept Introduction:

Conversion formula;

$\begin{array}{l}1troyoz(troyounce)Au=31.103gAu\\ 1pound(Ib)=453.6g\\ 1pound(Ib)=16ounce(oz)\end{array}$

Explanation of Solution

To determine: The mass of gold coin in grams

The unit of troy ounce is used for metal such as gold and platinum.  A gold coins weights 2.41 troy ounce.  Mass of gold coin in grams can be calculated by using conversion formula.

That is,

$1troyoz(troyounce)Au=31.103gAu$

So,

$\text{2}\text{.41}\text{troy}\text{oz}\text{Au}\text{×}\frac{\text{31}\text{.103}\text{g}\text{Au}}{\text{1}\text{troy}\text{oz}\text{Au}}\text{=}\text{75}\text{.0}\text{g}\text{Au}$

Interpretation Introduction

Interpretation:

From the given data’s, it should be calculated the mass of gold coinin grams and it should be checked whether a troy ounce is heavier or lighter than an ounce.

Concept Introduction:

Conversion formula;

$\begin{array}{l}1troyoz(troyounce)Au=31.103gAu\\ 1pound(Ib)=453.6g\\ 1pound(Ib)=16ounce(oz)\end{array}$

Explanation of Solution

To check: Whether a troy ounce is heavier or lighter than an ounce.

By using conversion factor, it can be check whether a troy ounce is heavier or lighter than an ounce.

That is, 1 troy oz should be converted to gram and the 1 gram should be converted to pound .at last 1 pound should be converted to ounce.

$\text{1 troy oz}\to \text{g}\to \text{Ib}\to \text{oz}$

$\begin{array}{l}1troyoz(troyounce)Au=31.103gAu\\ 1pound(Ib)=453.6g\\ 1pound(Ib)=16ounce(oz)\end{array}$

So the conversion can be done as follows;

$\begin{array}{l}\text{1}\text{troy}\text{oz}\text{Au}\text{×}\frac{\text{31}\text{.103}\text{g}\text{Au}}{\text{1}\text{troy}\text{oz}\text{Au}}\text{×}\frac{\text{1}\text{Ib}}{\text{453}\text{.6}\text{g}}\text{×}\frac{\text{16}\text{ounce}}{\text{1}\text{Ib}}\text{=}\text{1}\text{.097}\text{oz}\\ \text{That}\text{is,}\text{1}\text{troy}\text{oz}\text{=}\text{1}\text{.097}\text{oz}\end{array}$

So, it can be concluded that A troy ounce is heavier than an ounce