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Chapter 1: Problem 45

Precious metals and gems are measured in troy weights in the English system: \(\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \text { grain } &=0.0648 \text { gram } \\ 1 \text { carat } &=0.200 \mathrm{gram} \end{aligned}\) a. The most common English unit of mass is the pound avoirdupois. What is one troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

Short Answer

Expert verified
a. 1 troy pound is approximately \(0.373 \mathrm{~kg}\) and \(0.822 \mathrm{~lb}\). b. 1 troy ounce of gold weighs approximately \(31.1 \mathrm{~g}\) and \(155.5 \mathrm{~ct}\). c. The volume of a troy pound of gold is approximately \(176.71 \mathrm{~cm}^{3}\).

Step by step solution

01

Convert troy pound to grains

First, let's convert one troy pound to grains using the given conversion rates: 1 troy pound = 12 troy ounces, and 1 troy ounce = 20 pennyweights, and 1 pennyweight = 24 grains. So, 1 troy pound = 12 troy ounces * 20 pennyweights/troy ounce * 24 grains/pennyweight.
02

Convert grains to grams

Now, we will convert the result from step 1 from grains to grams: 1 grain = 0.0648 grams. So, 1 troy pound in grams = (12 * 20 * 24) * 0.0648 grams.
03

Convert grams to kilograms and pounds

Finally, we will convert the result from step 2 to kilograms and pounds: 1 kilogram = 1000 grams, and 1 pound = 453.592 grams. So, 1 troy pound in kilograms = (12 * 20 * 24 * 0.0648) / 1000 kg, and 1 troy pound in pounds = (12 * 20 * 24 * 0.0648) / 453.592 lb. b. Convert the mass of a troy ounce of gold to grams and carats.
04

Convert troy ounce to grams

First, we will convert one troy ounce to grams: 1 troy ounce = 20 pennyweights, and 1 pennyweight = 24 grains, and 1 grain = 0.0648 grams. So, 1 troy ounce in grams = 20 * 24 * 0.0648 grams.
05

Convert grams to carats

Now, we will convert the result from step 1 to carats: 1 carat = 0.200 grams. So, 1 troy ounce of gold in carats = (20 * 24 * 0.0648) / 0.200 carats. c. Find the volume of a troy pound of gold, given its density.
06

Calculate the mass of a troy pound of gold in grams

From part a, we already know that one troy pound of gold is equal to (12 * 20 * 24 * 0.0648) grams.
07

Use the density to find the volume

Now, we will use the given density of gold to find the volume of a troy pound of gold: Density of gold = 19.3 g/cm³. So, Volume = Mass / Density. Volume = (12 * 20 * 24 * 0.0648) / 19.3 cm³.

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Most popular questions from this chapter

A copper wire (density \(=8.96 \mathrm{~g} / \mathrm{cm}^{3}\) ) has a diameter of \(0.25 \mathrm{~mm}\). If a sample of this copper wire has a mass of \(22 \mathrm{~g}\), how long is the wire?

Use the following exact conversion factors to perform the stated calculations: $$ \begin{aligned} 5 \frac{1}{2} \text { yards } &=1 \text { rod } \\ 40 \text { rods } &=1 \text { furlong } \\ 8 \text { furlongs } &=1 \mathrm{mile} \end{aligned} $$ a. The Kentucky Derby race is \(1.25\) miles. How long is the race in rods, furlongs, meters, and kilometers? b. A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Perform the following mathematical operations and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation. a. \(0.00034159\) to three digits b. \(103.351 \times 10^{2}\) to four digits c. \(17.9915\) to five digits d. \(3.365 \times 10^{5}\) to three digits

The density of pure silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). If \(5.25 \mathrm{~g}\) of pure silver pellets is added to a graduated cylinder containing \(11.2 \mathrm{~mL}\) of water, to what volume level will the water in the cylinder rise?
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