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The Solid Phase Help (page 3)

By — McGraw-Hill Professional
Updated on Sep 5, 2011

The Solid Phase Practice Problems

Problem 1

A sample of solid matter has a volume of 45.3 cm 3 and a mass of 0.543 kg. What is the density in grams per centimeter cubed?

Solution 1

This problem is a little tricky because two different systems of units are used, SI for the volume and cgs for the mass. To get a meaningful answer, we must be consistent with our units. The problem requires that we express the answer in the cgs system, so we convert kilograms to grams. This means that we have to multiply the mass figure by 1,000, which tells us that the sample mass is 543 g. Determining the density in grams per centimeter cubed is now a simple arithmetic problem: Divide the mass by the volume. If d is density, m is mass, and v is volume,

d = m/v

In this case,

d = 543/45.3 = 12.0 g/cm 3

This answer is rounded to three significant figures.

Problem 2

Calculate the density of the sample from Problem 1 in kilograms per meter cubed. Do not use the conversion factor on the result of Problem . Start from scratch.

Solution 2

This requires that we convert the volume to units in SI, that is, to meters cubed. There are 1 million, or 10 6 , centimeters cubed in a meter cubed. Therefore, in order to convert this cgs volume to volume in SI, we must divide by 10 6 or multiply by 10 −6 . This gives us 45.3 × 10 −6 m 3 , or 4.53 × 10 −5 m 3 in standard scientific notation, as the volume of the object. Now we can divide the mass by the volume directly:

d = m/v

= 0.543/(4.53 × 10 −5 )

= 0.120 × 10 5

= 1.20 × 10 4 kg/m 3

This was rounded to three significant figures when the numerical division was performed.

Practice problems of these concepts can be found at: Basic States Of Matter Practice Test

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