Problem 32 - General Chemistry: Principles and Modern Applications

Question

Which is the greater mass, \(3257 \mathrm{mg}\) or \(0.000475 \mathrm{kg} ?\) Explain.

Step-by-Step Solution

Answer

After converting the mass units to be the same, it is determined that \(3257 \mathrm{mg}\) is greater than \(0.000475 \mathrm{kg}\).

Step 1: Conversion to Same Units

It would be easier to convert \(3257 \mathrm{mg}\) to \(\mathrm{kg}\) to make the comparison easier. We know that 1 \(\mathrm{kg}\) equals to \(1,000,000 \mathrm{mg}\), so we can convert \(3257 \mathrm{mg}\) to \(\mathrm{kg}\) by dividing by \(1,000,000\). The operation would be \(3257 \div 1,000,000 = 0.003257 \mathrm{kg}\).

Step 2: Comparing the Converted Masses

Now that both masses are in the same unit (\(\mathrm{kg}\)), comparing them is straightforward. We compare \(0.003257 \mathrm{kg}\) (converted from \(3257 \mathrm{mg}\)) to \(0.000475 \mathrm{kg}\) . We can clearly see that \(0.003257 \mathrm{kg}\) is greater than \(0.000475 \mathrm{kg}\).

Key Concepts

Understanding Unit Conversion

Unit conversion is an essential skill in math and science that allows us to compare quantities measured in different units. It involves altering the form of a number without changing its value. For mass, different units such as milligrams (mg), grams (g), and kilograms (kg) are often used.
To convert between them, it's crucial to know the conversion factors. For example,:

• 1 gram (g) is equal to 1,000 milligrams (mg).
• 1 kilogram (kg) is equal to 1,000 grams (g).
• Thus, 1 kilogram is equal to 1,000,000 milligrams.

This knowledge helps to standardize measurements across various systems, making it easier to perform calculations or comparisons. Keeping these factors in mind can make unit conversion straightforward.

Converting Milligrams to Kilograms

When you have a mass given in milligrams and you need to convert it to kilograms, the process requires dividing the mass in milligrams by the conversion factor of a kilogram in milligrams, which is 1,000,000. This conversion is crucial when dealing with significant differences in size between the two units.

The Conversion Process

- Begin with your value in milligrams. - Divide this value by 1,000,000.For example, if you have 3257 mg and you want to convert it to kg:\[3257 \div 1,000,000 = 0.003257 \text{ kg}\]This conversion helps in simplifying problems where comparisons or further calculations are needed in kilograms, the base SI unit for mass.

Comparing Masses After Conversion

Once all the mass values are in the same unit, comparing them becomes a simple task. In the scenario where you have converted 3257 mg to 0.003257 kg, and you need to compare it to another mass of 0.000475 kg, the larger number represents the greater mass.

• 0.003257 kg (from 3257 mg)
• 0.000475 kg (initial mass)

You can see that 0.003257 is clearly larger than 0.000475.
Therefore, the original mass of 3257 mg is greater than the 0.000475 kg.
This comparison method is effective because it ensures accuracy when assessing which of two measured quantities is larger, thus facilitating correct decision-making in scientific and mathematical analyses.