Density and Percent Composition Their Use in Problem Solving

Nine and a half months after launch, the MCO was to fire its main engine to achieve an elliptical orbit around Mars. The MCO engine start occurred on September 23, 1999, but the MCO mission was lost when the orbiter entered the Martian atmosphere on a lower-than-expected trajectory. The MCO entered the low orbit because the computer on Earth used British Engineering units, whereas the MCO computer used SI units. 

This error in units brought the MCO 56 km above the surface of Mars instead of the desired 250 km. At 250 km, the MCO would have successfully entered the desired elliptical orbit, and the 168 million orbiter would probably not have been lost. 

A The development of science requires careful quantitative measurement. Theories have stood or fallen based on their agreement or otherwise with experiments in the fourth significant figure or beyond. Problem solving, the handling of units, and the use of significant figures (Section 1-7) are important in all areas of science. 

Throughout this text, we will encounter new concepts about the structure and behavior of matter. One means of firming up our understanding of these new concepts is to work problems that relate concepts that we already know to those we are trying to understand. In this section, we will introduce two quantities frequently required in problem solving density and percent composition. 

Mass and volume are both extensive properties. An extensive property is dependent on the quantity of matter observed. However, if we divide the mass of a substance by its volume, we obtain density, an intensive property. An intensive property is independent of the amount of matter observed. Thus, the density of pure water at 25 °C has a unique value, whether the sample fills a small beaker (small mass/small volume) or a swimming pool (large mass/large volume). Intensive properties are especially useful in chemical studies because they can often be used to identify substances. 

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Density and Percent Composition Their Use in Problem Solving 1-6 Uncertainties in Scientific Measurements 1-7 Significant Figures... 

Density and Percent Composition Their Use in Problem Solving—Mass and volume are extensive properties they depend on the amount of matter in a sample. Density, the ratio of the mass of a sample to its volume, is an intensive property, a property independent of the amount of matter sampled. Density is used as a conversion factor in a variety of calculations. 

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