Question

Convert each mass measurement to its equivalent in kilograms. (Chapter 2) \(\begin{array}{ll}{\text { a. } 247 \mathrm{g}} & {\text { c. } 7.23 \mathrm{mg}} \\ {\text { b. } 53 \mathrm{mg}} & {\text { d. } 975 \mathrm{mg}}\end{array}\)

Short answer

The converted mass measurements are: a. \(0.247 \, kg\), b. \(0.000053 \, kg\), c. \(0.00000723 \, kg\), and d. \(0.000975 \, kg\).

Step-by-step solution

1. Convert a. 247 g to kg

To convert from grams to kilograms, divide by 1000. By doing this, we get: \(247 \, g = 247 / 1000 \, kg\)

2. Calculate the result

\(247 / 1000 = 0.247 \, kg\)

3. Convert b. 53 mg to kg

To convert from milligrams to kilograms, first divide by 1000 to convert milligrams to grams, then divide by 1000 again to convert grams to kilograms: \(53 \, mg = 53 / 1000 \, g = 53 / 1000 / 1000 \, kg \)

4. Calculate the result

\(53 / 1000 / 1000 = 0.000053 \, kg\)

5. Convert c. 7.23 mg to kg

To convert from milligrams to kilograms, apply the same procedure as in step 3: \(7.23 \, mg = 7.23 / 1000 \, g = 7.23 / 1000 / 1000 \, kg\)

6. Calculate the result

\(7.23 / 1000 / 1000 = 0.00000723 \, kg\)

7. Convert d. 975 mg to kg

To convert from milligrams to kilograms, apply the same procedure as in step 3: \(975 \, mg = 975 / 1000 \, g = 975 / 1000 / 1000 \, kg\)

8. Calculate the result

\(975 / 1000 / 1000 = 0.000975 \, kg\) So, after converting each mass measurement to its equivalent in kilograms, we get: a. \(0.247 \, kg\) b. \(0.000053 \, kg\) c. \(0.00000723 \, kg\) d. \(0.000975 \, kg\)

Key concepts

Unit Conversion

Understanding unit conversion is essential in various fields, from everyday life to scientific research. It’s the process of changing one unit of measure to another.
For the exercise at hand, we see the conversion of mass measurements in grams and milligrams to their equivalents in kilograms. The fundamental step is to recognize the conversion factors: 1 gram is equal to 0.001 kilograms (or 1/1000), and 1 milligram is equal to 0.000001 kilograms (or 1/1000/1000). By using these conversion factors, you can multiply any given value by the corresponding factor to convert one unit to another.
In educational settings, practicing unit conversions reinforces students’ understanding of the relationships between different units and hones their mathematical skills, key aspects of chemistry education and beyond.

Metric System

The metric system is an international system of measurement based on multiples of ten, also known as the International System of Units (SI). It is widely used around the world and in scientific communities because of its simplicity and ease of use.
For mass, the metric system primarily uses kilograms, grams, and milligrams. Each unit is a factor of ten larger or smaller than the next, which streamlines the process of unit conversion. Grams and kilograms are typical units for more extensive quantities, while milligrams are used for smaller, more precise measurements. Familiarity with the metric system is crucial in both education and professional life as it is the standard in many contexts internationally.

Dimensional Analysis

Dimensional analysis, also known as the factor-label method, is a powerful tool widely used in chemistry to convert from one unit to another. It involves using conversion factors that are constructed from equivalencies between different units.
A conversion factor can be represented as a fraction in which the numerator and denominator are equal quantities expressed in different units. For instance, in the exercise provided, the conversion factor from grams to kilograms is \(\frac{1 kg}{1000 g}\) and from milligrams to kilograms is \(\frac{1 kg}{1,000,000 mg}\). By multiplying the mass value by the appropriate conversion factor, the units we want to cancel out are divided, leaving us with the desired units. This methodical approach minimizes errors and ensures accuracy in conversions.

Chemistry Education

Chemistry education lays down the foundation for understanding the basic principles that govern the composition, structure, properties, and changes of matter.
One such fundamental topic is unit conversion within the metric system, vital for accurate measurements and calculations in experiments.

Effective Pedagogy

Using a systematic approach such as dimensional analysis ensures that students don’t just memorize steps but actually understand the underlying concepts. This comprehension is critical for their development as learners and future scientists.

Critical Thinking and Problem Solving

Engaging with exercises like the given mass conversion problem enhances critical thinking and problem-solving skills. Teachers should continually provide varied and practical examples to help students apply these skills in diverse scenarios, an integral part of effective chemistry education.