Calculate Mass from Density Example Problem

Calculate Mass from Density Example Problem Density is the amount of matter, or mass, per unit volume. This example problem shows how to calculate the mass of an object from a known density and volume. Simple Example (Metric Units) As an example of a simple problem, find the mass of a piece of metal that has a volume of 1.25  m3 and a density of 3.2 kg/m3. First, you should notice both the volume and the density use the volume of cubic meters. That makes the calculation easy. If the two units were not the same, youd need to convert one or the other of them so that they would be in agreement. Next, rearrange the formula for density to solve for mass. Density Mass à ·Ã‚  Volume Multiply both sides of the equation by volume to get: Density x Volume Mass or Mass Density x Volume Now, plug in the numbers to solve the problem: Mass 3.2 kg/m3 x 1.25 m3 If you see the units wont cancel out, then you know you did something wrong! If that happens, rearrange the terms until the problem works. In this example, cubic meters cancels out, leaving kilograms, which is a mass unit. Mass 4 kg Simple Example (English Units) Find the mass of a blob of water with a volume of 3 gallons. It seems easy enough, right? Most people memorize the density of water as 1... but thats in grams per cubic centimeters! Fortunately, its easy to look up the density of water in any units. Density of Water 8.34 lb/gal So, the problem becomes: Mass 8.34 lb/gal x 3 gal Mass 25 lb Problem The density of gold is 19.3 grams per cubic centimeter. What is the mass of a bar of gold in kilograms that measures 6 inches x 4 inches x 2 inches? Solution Density is equal to the mass divided by the volume.D m/VwhereD densitym massV volumeWe have the density and enough information to find the volume in the problem. All that remains is to find the mass. Multiply both sides of this equation by the volume, V and get:m DVNow we need to find the volume of the gold bar. The density we have been given is in grams per cubic centimeter but the bar is measured in inches. First we must convert the inch measurements to centimeters.Use the conversion factor of 1 inch 2.54 centimeters.6 inches 6 inches x 2.54 cm/1 inch 15.24 cm.4 inches 4 inches x 2.54 cm/1 inch 10.16 cm.2 inches 2 inches x 2.54 cm/1 inch 5.08 cm.Multiply all three of these numbers together to get the volume of the gold bar.V 15.24 cm x 10.16 cm x 5.08 cmV 786.58 cm3Place this into the formula above:m DVm 19.3 g/cm3 x 786.58 cm3m 14833.59 gramsThe answer we want is the mass of the gold bar in kilograms. There are 1000 grams in 1 kilogram, so:mass in kg mass in g x 1 kg/1000 gmass in kg 14833.59 g x 1 kg/1000 gmass in kg 14.83 kg. Answer The mass of the gold bar in kilograms measuring 6 inches x 4 inches x 2 inches is 14.83 kilograms. Tips for Success The biggest problem students make when solving for mass is not setting up the equation correctly. Remember, mass equals density multiplied by volume. This way, the units for volume cancel out, leaving the units for mass.Be sure the units used for volume and density work together. In this example, mixed metric and English units were intentionally used to show how to convert between units.Volume units, in particular, can be tricky. Remember, when you determine volume, you need to apply the correct formula. Summary of Density Formulas Remember, you can arrange one formula to solve for mass, density, or volume. Here are the three equations to use: Mass Density x VolumeDensity Mass  Ãƒ · VolumeVolume Mass  Ãƒ ·Ã‚  Density Learn More For more example problems, use the Worked Chemistry Problems. It contains over a hundred different worked example problems useful for chemistry students. This density example problem shows how to calculate the density of a material when the mass and volume are known.This example problem shows how to find the density of an ideal gas when given the molecular mass, pressure, and temperature.This example problem shows the steps necessary to convert inches to centimeters. Source CRC Press Handbook of Tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59.