Using Density as a Conversion Factor

The density of a substance is an equality from which conversion factors can be derived. For example, the density of gold (from Table 2.7) is 19.3 g/mL. In other words, 

This gives us the conversion factors that can be used to convert any number of milliliters of gold to grams, or any number of grams of gold to milliliters. 

In other words, density can be used to determine the volume that a certain number of grams of a substance occupies, or the mass of a certain volume of a substance. The conversion factors are as follows. 

What is the mass of 7.84 ml (measured at 20°C) of ethyl alcohol Solution 2.11 

From Table 2.7, the density of ethyl alcohol at 20°C is 0.789 g/mL. The mass of 7.84 ml of ethyl alcohol is calculated as follows  

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A 4.028 m solution of ethylene glycol in water contains 4.028 mol of ethylene glycol per kilogram of water. To find the solution s molarity, we need to find the number of moles of solute per volume (liter) of solution. The volume, in turn, can be found from the mass of the solution by using density as a conversion factor. 

The volume of the solution is obtained from its mass by using density as a conversion factor ... 

You are probably well aware that the pressures at great depths under the ocean are extremely large, and the deeper you go, the greater the pressure that is exerted. Let s start small and look at a beaker filled with water. The beaker has a diameter of 10 cm, and the height of the water is 20 cm. How much pressure does the water exert on the bottom of the beaker To answer this question we simply need to recall that P = FI A. The force involved is the weight of the water contained in the beaker. The weight of the water can be calculated from the mass of the water, and the mass of the water can be calculated from the volume, using density as a conversion factor. 

Use density as a conversion factor to convert between mass and volume. 

To find the number of moles of octane in one liter, use density as a conversion factor to find grams of octane, then use the molar mass of octane to convert to moles of octane. The strategy is ... 

Solution Our first step is to calculate the mass of water in one liter of the solution, using density as a conversion factor. The total mass of 1 L of a 2.45 M solution of methanol is... 

You can use density as a conversion factor between volume and mass. For example, given that water has a density of 1.00 g/cm, what is the mass of 350 cm of water ... 

Writing Conversion Factors from Equalities 42 Using Conversion Factors 48 Using Density as a Conversion Factor 58 Classifying Matter 70... 

If we measure the mass of an object and its volume, simple division gives us its density. Conversely, if we know the density of an object, we can use density as a conversion factor to determine the object s mass or volume. For example, a cube of osmium 1.000 cm on edge weighs 22.59 g. The density of osmium (the densest of the elements) is 22.59 g/cm. What would be the mass of a cube of osmium that is 1.25 inches on edge (1 in = 2.54 cm) To solve this problem, we begin by relating the volume of a cube to its length, that is, V = Then we can map out... 

Examples 1-2 and 1-3 further illustrate that numerical calculations involving density are generally of two types determining density from mass and volume measurements and using density as a conversion factor to relate mass and volume. 

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