Problem 31 - General Chemistry: Principles and Modern Applications

Question

Which is the greater mass, \(3245 \mu \mathrm{g}\) or \(0.00515 \mathrm{mg} ?\) Explain.

Step-by-Step Solution

Answer

The greater mass is \(3245 \mu g\).

Step 1: Understanding the Conversion Rates

First, understand the conversion rates. There are \(1,000,000 \mu g \) in a gram and 1000 milligrams in a gram. Therefore, \(1mg = 1000 \mu g\).

Step 2: Convert the Given Values to the Same Unit

Convert the given value of 0.00515 milligrams to micrograms using the conversion rate \(1mg = 1000 \mu g\). So, \(0.00515 mg = 0.00515 \times 1000 \mu g = 5.15 \mu g\)

Step 3: Comparison of Two Masses

Now that both masses are in the same unit, they can easily be compared. The comparison between \(3245 \mu g\) and \(5.15 \mu g \) shows that \(3245 \mu g\) is greater than \(5.15 \mu g \).

Key Concepts

Mass Comparison

Comparing mass involves examining different weights to determine which one is larger. When dealing with very small quantities like micrograms (\( \mu g \)) and milligrams (\( mg \)), direct comparison can be tricky because they are such small units.By converting each measurement to the same unit, it simplifies the comparison. When both numbers are in micrograms or milligrams, you can easily discern which is greater. In our specific problem, converting both values to micrograms makes it apparent that \( 3245 \mu g \) is larger than \( 5.15 \mu g \).Remember, a larger numeric value in the same unit typically indicates a greater mass.

Micrograms to Milligrams

Understanding how to convert between micrograms (\( \mu g \)) and milligrams (\( mg \)) is essential when you work with measurements in the metric system. The conversion is straightforward:

• 1 milligram is equivalent to 1000 micrograms (\( 1 \, mg = 1000 \mu g \)).
• To convert milligrams to micrograms, you simply multiply by 1000.

For instance, if you have \( 0.00515 \, mg \), multiply by 1000 to convert to micrograms:\[0.00515 \, mg \times 1000 = 5.15 \, \mu g\]This ensures both measurements are in terms of micrograms, allowing for a direct and meaningful comparison.

Metric System Conversion

The metric system is used worldwide for its simplicity and ease of conversion between units. All units are based on powers of ten, which makes conversions straightforward. When you're given masses in different metric units, like in this exercise with micrograms and milligrams, it's important to convert them into the same unit before performing any comparisons.

• Grams are a common base unit in the metric system. There are 1000 micrograms (\( \mu g \)) in a milligram (\( mg \)) and 1,000,000 micrograms in a gram.
• To convert from one unit to another, identify how many of the smaller unit make up the larger unit, then multiply or divide as needed.

This structure makes unit conversions consistent and reliable, helping you understand and compare different units of measure effectively. Understanding these conversions ensures accuracy in any scientific, medical, or mathematical setting you engage in.