Problem 60 - Chemistry: Atoms First

Question

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Step-by-Step Solution

Answer

The conversion factor is 978 grams / 34.5 ounces = 28.3478 grams/ounce, which can be justified to three significant figures: 28.3 grams/ounce.

Step 1: Understand the Problem

The problem provides the mass of the cereal in both grams and ounces. The task is to find a conversion factor that will allow us to convert grams to ounces and vice versa.

Step 2: Calculate the Conversion Factor

To find the conversion factor, divide the mass in grams by the mass in ounces, which is given as 978 grams over 34.5 ounces.

Step 3: Perform the Division

Dividing 978 grams by 34.5 ounces gives the conversion factor in grams per ounce.

Step 4: Consider Significant Figures

Both measurements are given to three significant figures, so the conversion factor should also be reported with three significant figures to reflect the precision of the data.

Key Concepts

Significant Figures

Understanding significant figures is crucial in chemistry, especially when making precise measurements. Significant figures refer to the digits in a number that carry meaning contributing to its precision. These include all nonzero digits, any zeros between significant digits, and trailing zeros in a decimal number. For example, in the measurement 978 grams, there are three significant figures: 9, 7, and 8.

When performing calculations, it's important to be mindful of significant figures, as the results should not have greater precision than the least precise measurement. In the given exercise, both the mass in grams and ounces are reported to three significant figures, which is why the conversion factor derived from these measurements must also be expressed with three significant figures. This avoids offering a false sense of precision and maintains the integrity of the data.

Metric to English Conversion

Unit conversion is an integral part of chemistry, allowing us to understand and compare quantities in different measurement systems. In our cereal box example, we're converting from the metric system (grams) to the English system (ounces). To do so, we apply a conversion factor which serves as a multiplier converting a quantity from one unit to another. This factor is a form of ratio or fraction that represents the equivalence of the two units.

When finding a conversion factor, choose one that allows for a clear conversion between units without altering the value, just the expression of that value. In the case of our exercise, the conversion factor is calculated by dividing the mass in grams by the equivalent mass in ounces, providing us a rate that can be used for any subsequent conversions.

Mass Conversion

Mass conversion between different unit systems, such as metric and English units, is fundamental in various scientific disciplines including chemistry. Mass is a measure of the amount of matter in an object, and understanding how to convert this measure is essential for tasks ranging from following recipes to conducting complex experiments.

Since different regions and scientific communities use different units of measure, being able to accurately convert between them is a necessary skill. The aim is to express the mass, maintaining its actual value, across various unit systems. In our example, we've shown how to convert grams to ounces, but this is only one instance of mass conversion. Others include converting kilograms to pounds or milligrams to grains. To do this effectively, always use accurate conversion factors and clearly define the number of significant figures for precision.