Question

Gold A troy ounce is equal to 480 grains, and 1 grain is equal to 64.8 milligrams. If the price of gold is \(\$ 560\) per troy ounce, what is the cost of 1 \(\mathrm{g}\) of gold?

Short answer

The cost of 1 gram of gold is \(\$18\).

Step-by-step solution

Find the price of gold per grain

First, we need to convert the price of gold per troy ounce to the price of gold per grain. We are given that 1 troy ounce equals 480 grains and the price of gold is \(\$ 560\) per troy ounce. To find the price per grain, we can use the equation: Price per grain = Price per troy ounce / Number of grains per troy ounce Price per grain = \(\$560 / 480\) Price per grain = \(\$1.1667\)

Find the price of gold per milligram

Next, we need to convert the price of gold per grain to the price of gold per milligram. We are given that 1 grain is equal to 64.8 milligrams. To find the price per milligram, we can use the equation: Price per milligram = Price per grain / Number of milligrams per grain Price per milligram = \(\$1.1667 / 64.8\) Price per milligram = \(\$0.018\)

Find the price of gold per gram

Finally, we need to convert the price of gold per milligram to the price of gold per gram. We know that there are 1000 milligrams in 1 gram. To find the price per gram, we can use the equation: Price per gram = Price per milligram * Number of milligrams per gram Price per gram = \(\$0.018 * 1000\) Price per gram = \(\$18\) Thus, the cost of 1 gram of gold is \(\$18\).

Key concepts

Troy Ounce Conversion

Understanding the troy ounce is fundamental when dealing with precious metals, like gold and silver. Unlike the more common avoirdupois ounce that we use for everyday items, which is approximately 28.35 grams, a troy ounce is heavier, at approximately 31.1 grams.

The troy ounce has been traditionally used in the measurement and pricing of precious metals. It dates back to the Roman monetary system, where the currency was based on bronze bars. Conversions often come up in chemistry when dealing with compounds that have metallic elements, which may be traded in troy ounces.

To visualize the conversion, imagine a finely balanced scale; on one side, you have a troy ounce, and on the other, 480 grains. Each grain is a small unit of mass, equal to about 64.8 milligrams. This concept of the troy ounce and grain is essential in chemistry when precise measurements of compounds are needed, and the economic aspect, as seen in the gold pricing.

Unit Conversion

Unit conversion is a multipurpose tool in both chemistry and mathematics, allowing us to translate different units of measurement to one another. The step by step example provided illustrates how unit conversions can be used to find the cost of gold per gram from a price per troy ounce.

In chemistry, unit conversion is not just limited to mass; it includes volume, length, time, and temperature, among others. Understanding and mastering this skill is crucial for students to grasp because it enables you to approach problems in a structured way and find solutions that require converting units from one system to another.

Remembering conversion factors, like '1 gram equals 1000 milligrams' or '1 troy ounce equals 480 grains', is often a starting point. The real mastery comes in applying these conversions to solve real-world problems. It's like a puzzle where each piece is a unit, and fitting them together gives you a complete picture of the solution.

Chemistry in Everyday Life

Chemistry is not confined to lab experiments; it's all around us, in everything we do and see, including economics and market pricing. The problem of converting the cost of gold from troy ounces to grams is a prime example of chemistry intersecting with daily life. Gold is a chemical element, and its market pricing, while influenced by many factors, is an exercise in applied chemistry.

For instance, calculating medication dosage, mixing ingredients for a cake, or even enjoying the colors of a sunset are all applications of chemistry. It teaches us the composition and properties of substances and how substances interact with one another. So, every time you see an item sold by weight, remember that the underlying chemical properties and standardized units are what make fair trade possible.

Therefore, understanding chemistry is essential to making smart decisions, from purchasing gold to following a recipe. This shows the interconnectedness of scientific concepts with real-world applications, emphasizing how valuable a working knowledge of chemistry is in our everyday lives.