Problem 39 - Chemistry The Central Science In Si Units

Question

If on a certain year, an estimated amount of 4 million metric tons (1 metric ton \(=1000 \mathrm{~kg}\) ) of nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) was emitted worldwide due to agricultural activities, express this mass of \(\mathrm{N}_{2} \mathrm{O}\) in grams without exponential notation, using an appropriate mètric préfix.

Step-by-Step Solution

Answer

The mass is 4 teragrams (Tg).

Step 1: Understand the Problem

We need to convert 4 million metric tons of nitrous oxide emissions into grams, using an appropriate metric prefix, without using exponential notation.

Step 2: Convert Metric Tons to Kilograms

Since 1 metric ton is equal to 1000 kg, we multiply 4 million metric tons by 1000 kg/metric ton to find out the mass in kilograms:\[4,000,000 \text{ metric tons} \times 1000 \frac{\text{kg}}{\text{metric ton}} = 4,000,000,000 \text{ kg}\]

Step 3: Convert Kilograms to Grams

Next, we convert the mass from kilograms to grams. There are 1000 grams in a kilogram:\[4,000,000,000 \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 4,000,000,000,000 \text{ g}\]

Step 4: Use an Appropriate Metric Prefix

The resulting mass is 4 trillion grams. In metric terms, this is expressed as teragrams (Tg), where 1 teragram = 1 trillion grams. Therefore, the mass in teragrams is:\[4,000,000,000,000 \text{ g} = 4 \text{ Tg}\]

Key Concepts

metric tons to grams

When converting metric tons to grams, it's important to first understand the basic relationship between them. A metric ton and a gram are both part of the metric system, which is a system of measurement commonly used around the world, based on powers of ten. A metric ton is a large unit of mass compared to a gram. Here's the conversion breakdown:

• 1 metric ton = 1000 kilograms (kg)
• 1 kilogram = 1000 grams (g)

To convert from metric tons to grams, you need to multiply the number of metric tons by 1,000,000 (since 1 metric ton is equal to 1,000 kg, and each kilogram is 1,000 grams).
In this problem, 4 million metric tons converts to grams this way:

• First, convert 4 million metric tons to kilograms by multiplying 4,000,000 by 1,000.
• Then convert kilograms to grams by multiplying the result by 1,000.
• This results in 4,000,000,000,000 grams.

This straightforward conversion is a great way to exercise the principle of working within the metric system.

metric prefix

Metric prefixes are extremely useful for expressing very large or very small numbers in a simplified way. They follow a base 10 system, allowing for easy scaling of units without losing precision. Some common metric prefixes include:

• Kilo (k) - 1,000 or 10³
• Mega (M) - 1,000,000 or 10⁶
• Giga (G) - 1,000,000,000 or 10⁹
• Tera (T) - 1,000,000,000,000 or 10¹²

In the case of converting 4 trillion grams, it's appropriate to use the teragram (Tg). Here, "tera" indicates a factor of a trillion or 10¹².
Representing a large number like 4,000,000,000,000 grams as 4 teragrams (4 Tg) simplifies the expression and makes it easier to communicate and use practically.

unit conversion

Unit conversion is a key skill in many scientific and engineering fields. It involves converting quantities expressed in one unit to another, to better align with the contexts or preferences of the task at hand.
Key steps in unit conversion:

• Identify the units you are converting from and to.
• Know the conversion factor between the units (e.g., 1 kg = 1000 g).
• Multiply or divide the quantity by the conversion factor(s) to get the desired unit.

In converting metric tons to grams, and then using a metric prefix, we demonstrated unit conversion through multiplying and applying appropriate factors such as 1,000 and 1,000,000,000,000 in successive steps.
Developing a strong understanding of these conversion processes will allow you to apply them across different contexts, ensuring precision and clarity in your calculations and results.