Problem 142 - General Chemistry

Question

One year of world production of gold was \(49.6 \times 10^{6}\) troy ounces. One troy ounce equals \(31.10 \mathrm{~g}\). What was the world production of gold in metric tons \(\left(10^{6} \mathrm{~g}\right)\) for that year?

Step-by-Step Solution

Answer

The world production of gold was 1542.56 metric tons.

Step 1: Understand the Conversion

This problem asks us to convert from troy ounces to metric grams, and then to metric tons. One troy ounce is equal to 31.10 grams. This conversion rate is crucial for our calculations.

Step 2: Calculate Total Production in Grams

First, we need to convert the total gold production from troy ounces to grams. Multiply the total production in troy ounces \(49.6 \times 10^6\) by the conversion factor, 31.10 grams per troy ounce.\[49.6 \times 10^6 \times 31.10 = 1,542,560,000\; ext{grams}.\]

Step 3: Convert Grams to Metric Tons

Since 1 metric ton is equal to \(10^6\) grams, divide the total grams by \(10^6\) to convert it into metric tons.\[\frac{1,542,560,000}{10^6} = 1542.56 \; ext{metric tons}.\]

Step 4: Express the Final Answer

The total annual production of gold in metric tons is 1542.56 metric tons.

Key Concepts

Troy Ounce to Grams Conversion

Converting from troy ounces to grams is the first critical step in transforming gold production measurements. A troy ounce, commonly used for precious metals, is slightly different than the standard ounce. One troy ounce equals exactly 31.10 grams, not to be confused with the avoirdupois ounce, which is about 28.35 grams. Understanding this distinction is vital when working with precious metals like gold.

To convert troy ounces into grams, simply multiply the number of troy ounces by 31.10. For instance, converting the world gold production of \(49.6 \times 10^6\) troy ounces into grams requires simple multiplication:

• Amount in troy ounces: \(49.6 \times 10^6\)
• Conversion factor: \(31.10\) grams per troy ounce
• Total in grams: \(49.6 \times 10^6 \times 31.10 \approx 1,542,560,000\)

This results in a total of 1,542,560,000 grams of gold produced annually.

Grams to Metric Tons Conversion

After converting gold production to grams, the next step is to translate that amount into metric tons for better manageability and understanding. A metric ton, also known as a tonne in other English-speaking regions, equals 1,000,000 grams or simply \(10^6\) grams. This makes it a convenient unit for expressing large quantities.

The process to convert grams to metric tons involves dividing the number of grams by 1,000,000. This conversion simplifies massive amounts into smaller, more understandable numbers.

• Total grams from previous conversion: 1,542,560,000 grams
• Conversion to metric tons: \(\frac{1,542,560,000}{10^6} = 1542.56\)

Converting the world production of gold into metric tons results in approximately 1542.56 metric tons for that year.

Metric Ton Calculation

Metric ton calculations enable us to express and work with large quantities of substances like gold more conveniently. Performing a metric ton calculation involves recognizing the essence of bulk conversion. Here, gram to metric ton conversion emphasizes just how large a metric ton is compared to gram-based measurements.

After performing the conversions from troy ounces to grams and grams to metric tons, metric ton calculations become straightforward. It sharpens the focus on understanding that 1 metric ton equals 1 million grams. Thus, after calculating the massive gold production amount in grams, dividing by \(10^6\) seamlessly offers the result in metric tons, simplifying comprehension.

• Calculated total in metric tons for the annual gold production: 1542.56 metric tons

These calculations highlight the vast capacity measurement of metric tons, delineating its essential use in representing large-scale productions efficiently.