Problem 44 - Chemistry The Molecular Nature of Matter

Question

What numbers should replace the question marks below? (a) \(1 \mathrm{nm}=? \mathrm{~m}\) (d) \(1 \mathrm{Mg}=? \mathrm{~g}\) (b) \(1 \mu \mathrm{g}=? \mathrm{~g}\) (e) \(1 \mathrm{mg}=? \mathrm{~g}\) (c) \(1 \mathrm{~kg}=? \mathrm{~g}\) (f) \(1 \mathrm{dg}=? \mathrm{~g}\)

Step-by-Step Solution

Answer

a) 1 nm = 1e-9 m, b) 1 Mg = 1e6 g, c) 1 \textmu g = 1e-6 g, d) 1 mg = 1e-3 g, e) 1 kg = 1e3 g, f) 1 dg = 1e-1 g

Step 1 - Converting Nanometers to Meters

To convert nanometers to meters, remember that 'nano' means 10^-9. So, 1 nanometer is 1 * 10^-9 meters.

Step 2 - Converting Megagrams to Grams

To convert megagrams to grams, note that 'mega' means 10^6. Therefore, 1 megagram is 1 * 10^6 grams.

Step 3 - Converting Micrograms to Grams

To convert micrograms to grams, understand that 'micro' means 10^-6. Thus, 1 microgram equals 1 * 10^-6 grams.

Step 4 - Converting Milligrams to Grams

Converting milligrams to grams requires the knowledge that 'milli' means 10^-3. So, 1 milligram is 1 * 10^-3 grams.

Step 5 - Converting Kilograms to Grams

For converting kilograms to grams, remember that 'kilo' means 10^3. Therefore, 1 kilogram is equal to 1 * 10^3 grams.

Step 6 - Converting Decigrams to Grams

Converting decigrams to grams means knowing that 'deci' stands for 10^-1. Hence, 1 decigram equals 1 * 10^-1 grams.

Key Concepts

Understanding Nanometer to Meter Conversion

To comprehend the nanometer to meter conversion, it's crucial to know that a nanometer is one billionth of a meter. The prefix 'nano' represents the factor of 10^{-9}. It's commonly used in chemistry and physics to measure atomic and molecular dimensions.

Here's an everyday analogy: If a marble were a nanometer, then one meter would be the size of the Earth. This conversion is pivotal in understanding the scale of atoms and the wavelengths of light.

The Basics of Megagram to Gram Conversion

When dealing with mass in larger units, megagrams to gram conversion is an essential skill. One megagram is equivalent to one million grams, expressed as 10^{6} grams. The prefix 'mega' is a massive scale, often used in geological or astronomical contexts.

Think about it in terms of cars. If a standard car weighs roughly a megagram, then converting to grams is like determining the weight of the car in kilograms, but on a scale 1000 times larger.

Microgram to Gram Conversion Simplified

Understanding the microgram to gram conversion is vital for measuring very small masses. A single microgram is one-millionth of a gram (0.000001 grams or 10^{-6} grams). In medicine and chemistry, this measurement is crucial for doses and chemical reactions.

For context, a single grain of salt weighs about 58 micrograms. The preciseness of this conversion is critical in pharmaceuticals where accurate dosing can be a matter of life and death.

Converting Milligrams to Grams

Milligrams to grams conversion is commonly used in everyday life, especially in nutrition labeling and medication. Since 'milli' means one-thousandth, 1 milligram is 10^{-3} grams. In other words, it takes 1000 milligrams to make up a gram.

A common real-world example is a pain reliever tablet, which is often dosed in milligrams, showing how we regularly use this conversion in practical situations.

Kilogram to Gram Conversion Basics

Kilograms to grams is a basic conversion that is essential to grasp, as many everyday items are measured in kilograms. The prefix 'kilo' stands for a thousand, making 1 kilogram equal to 10^{3} grams, or 1000 grams.

You might encounter this when measuring ingredients in the kitchen or checking baggage allowance for a flight, where the weight limit is typically given in kilograms.

Understanding Decigram to Gram Conversion

In the metric system, 'deci' indicates a tenth, so a decigram is 10^{-1} of a gram, or 0.1 grams. This unit isn't as commonly used, but understanding it allows for comprehensive knowledge of metric measurements. It can be helpful in scientific studies where precision at this scale is required.

An example might be a nutritionist balancing a diet plan to the nearest decigram to ensure an accurate calorie count and nutrient distribution.