Question

The unit "troy ounce" is often used for precious metals such as gold \((\mathrm{Au})\) and platinum \((\mathrm{Pt})(1\) troy ounce \(=\) \(31.103 \mathrm{~g}\) ). (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 \((1 \mathrm{lb}=16 \mathrm{oz} ; 1 \mathrm{lb}=453.6 \mathrm{~g}\) )?

Short answer

(a) 74.91 grams. (b) A troy ounce is heavier than a regular ounce.

Step-by-step solution

Understand the Conversion for Part (a)

We need to convert the mass from troy ounces to grams for a gold coin that weighs 2.41 troy ounces. Given that \(1\) troy ounce is equivalent to \(31.103\) grams, we can calculate the mass in grams.

Calculate the Mass in Grams

To find the mass in grams, multiply the number of troy ounces by the conversion factor from troy ounces to grams.\[\text{Mass in grams} = 2.41 \text{ troy ounces} \times 31.103 \text{ g/troy ounce}.\]Therefore, \[\text{Mass in grams} = 74.90683 \text{ g}.\]

Determine if a Troy Ounce is Heavier or Lighter

For part (b), we compare a troy ounce with a common ounce. A regular ounce's weight can be calculated by dividing the gram equivalent of a pound by 16 ounces:\[\text{Mass in grams per regular ounce} = \frac{453.6 \text{ g/pound}}{16 \text{ oz/pound}} = 28.35 \text{ g/oz}.\]Compare this with a troy ounce, which is \(31.103\) grams.

Draw Conclusions

Since a troy ounce (\(31.103\) g) is heavier than a regular ounce (\(28.35\) g), a troy ounce is heavier than a regular ounce.

Key concepts

Understanding the Troy Ounce

The term "troy ounce" is a special unit of weight that is predominantly used for precious metals like gold and platinum. While we often talk about ounces in everyday life, those are generally "avoirdupois" ounces.
The troy ounce is slightly heavier than a regular ounce, measuring 31.103 grams compared to an avoirdupois ounce at 28.35 grams. This difference is important in financial transactions involving gold, as even a small change can affect the value.
Understanding the difference between these two types of ounces is crucial when buying or evaluating precious metals. The troy ounce ensures a standardized, fair trade unit across the world in the precious metals market.

Accurate Mass Calculation

When calculating the mass of an object using different units, precision is key. In our example, a gold coin weighs 2.41 troy ounces. To find out how many grams that is, you simply multiply the number of troy ounces by the conversion factor from troy ounces to grams:

• \[\text{Mass in grams} = 2.41 \, \text{troy ounces} \times 31.103 \, \text{g/troy ounce}\]
• This gives us \[74.90683\, \text{grams}\].

By following these steps, you ensure accuracy in converting weights of gold and other precious metals, which is crucial for anything from jewelry making to investment.

Comparative Weight of Troy Ounce and Regular Ounce

When comparing the weight of a troy ounce to a regular avoirdupois ounce, it's essential to note that the troy ounce is heavier.
This comparison is significant when dealing with materials priced by weight, such as precious metals. \(31.103\) grams equals a troy ounce, while a regular ounce is only \(28.35\) grams.
This means that if you're buying gold measured in troy ounces, each unit is slightly heavier than what you might expect if you were used to the avoirdupois system.

Gold Mass Conversion Insight

When converting the mass of gold from troy ounces to grams, it is important to use precise conversion factors to avoid errors in calculations.
The basis for conversion when it comes to gold is always

• 1 troy ounce = 31.103 grams.

The conversion process is straightforward, but precise measurements are critical, especially when dealing with expensive items like gold.
Understanding and accurately applying the conversion factor ensures that you get the correct mass, which is vital for correct valuation, selling, and purchasing of gold. This knowledge underpins fair trading and can significantly affect financial decisions concerning precious metals.