Consider the jar of jelly beans in the photo. To get an estimate of the number of beans in the jar you weigh six beans and obtain masses of 3.15, 3.12, 2.98, 3.14, 3.02, and 3.09 g. Then you weigh the jar with all the beans in it, and obtain a mass of 2082 g. The empty jar has a mass of 653 g. Based on these data, estimate the number of beans in the jar. Justify the number of significant figures you use in your estimate.

Key Concepts

Mass and Weight Measurement

In chemistry, mass is a measure of the amount of matter in an object, typically measured in grams. Weight, while often used interchangeably with mass, refers to the force exerted by gravity on that mass. Accurate mass measurements are crucial for calculations in stoichiometry and determining quantities in chemical reactions.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This concept is essential in scientific measurements, as it reflects the certainty of the data collected. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures to maintain accuracy.

Estimation and Calculation of Quantity

Estimating the number of jelly beans involves calculating the total mass of the beans and then dividing by the average mass of a single bean. This process requires understanding how to manipulate mass data and apply basic arithmetic to derive a meaningful quantity. The average mass is calculated from the measured masses of the six beans, which is then used to estimate the total number of beans in the jar.