{"id":2135,"date":"2018-04-11T23:52:01","date_gmt":"2018-04-12T03:52:01","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/other-units-temperature-and-density\/"},"modified":"2019-06-20T14:04:47","modified_gmt":"2019-06-20T18:04:47","slug":"other-units-temperature-and-density","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/other-units-temperature-and-density\/","title":{"raw":"2.5 Density - Just Another Conversion Factor","rendered":"2.5 Density &#8211; Just Another Conversion Factor"},"content":{"raw":"<div class=\"section\" id=\"ball-ch02_s05\" lang=\"en\">\r\n<div class=\"learning_objectives editable block\" id=\"ball-ch02_s05_n01\">\r\n<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li><span style=\"font-size: 1em\">Define density and use it as a conversion factor.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"section\" id=\"ball-ch02_s05\" lang=\"en\">\r\n<p id=\"ball-ch02_s05_p14\" class=\"para editable block\"><span class=\"margin_term\"><a class=\"glossterm\">Density\u00a0<\/a><\/span>is a physical property that is defined as a substance\u2019s mass divided by its volume:<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\">density =\u00a0mass\/volume\u00a0\u00a0or\u00a0d = m\/V<\/span><\/p>\r\n<p id=\"ball-ch02_s05_p15\" class=\"para editable block\">Density is usually a measured property of a substance, so its numerical value affects the significant figures in a calculation. Notice that density is defined in terms of two dissimilar units, mass and volume. That means that density overall has derived units, just like velocity. Common units for density include g\/mL, g\/cm<sup class=\"superscript\">3<\/sup>, g\/L, kg\/L, and even kg\/m<sup class=\"superscript\">3<\/sup>. Densities for some common substances are listed in <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 \"Densities of Some Common Substances\"<\/a>.<\/p>\r\n\r\n<div class=\"table block\" id=\"ball-ch02_s05_t01\">\r\n<p class=\"title\"><strong><span class=\"title-prefix\">Table 1.<\/span><\/strong> Densities of Some Common Substances<\/p>\r\n\r\n<table style=\"border-spacing: 0px\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Substance<\/th>\r\n<th>Density (g\/mL or g\/cm<sup class=\"superscript\">3<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>water<\/td>\r\n<td>1.0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>gold<\/td>\r\n<td>19.3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>mercury<\/td>\r\n<td>13.6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>air<\/td>\r\n<td>0.0012<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>cork<\/td>\r\n<td>0.22\u20130.26<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>aluminum<\/td>\r\n<td>2.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>iron<\/td>\r\n<td>7.87<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"ball-ch02_s05_p16\" class=\"para editable block\">Because of how it is defined, density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm<sup class=\"superscript\">3<\/sup>. How can you determine what mass of aluminum you have without measuring it? You can use the volume to calculate it. If you multiply the given volume by the known density (from <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 \"Densities of Some Common Substances\"<\/a>), the volume units will cancel and leave you with mass units, telling you the mass of the sample:<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\"> 7.88\u00a0cm<sup>3<\/sup>\u2009\u00d7\u20092.7\u00a0g\/cm<sup>3\u00a0<\/sup>= 21\u00a0g\u00a0of\u00a0aluminum<\/span><\/p>\r\n<p id=\"ball-ch02_s05_p17\" class=\"para editable block\">where we have limited our answer to two significant figures.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Example 1<\/h3>\r\n<p id=\"ball-ch02_s05_p18\" class=\"para\">What is the mass of 44.6 mL of mercury?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p19\" class=\"para\">Use the density from <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 \"Densities of Some Common Substances\"<\/a> as a conversion factor to go from volume to mass:<\/p>\r\n<span class=\"informalequation\">44.6\u00a0mL\u2009\u00d7\u200913.6\u00a0g\/mL = 607\u00a0g<\/span>\r\n<p id=\"ball-ch02_s05_p20\" class=\"para\">The mass of the mercury is 607 g.<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p21\" class=\"para\">What is the mass of 25.0 cm<sup class=\"superscript\">3<\/sup> of iron?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p22\" class=\"para\">197 g<\/p>\r\n\r\n<\/div>\r\n<p id=\"ball-ch02_s05_p23\" class=\"para editable block\">Density can also be used as a conversion factor to convert mass to volume\u2014but care must be taken. We have already demonstrated that the number that goes with density normally goes in the numerator when density is written as a fraction. Take the density of gold, for example:<\/p>\r\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_3.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_3.png\" alt=\"d = 19.3 g\/1 mL\" width=\"225\" height=\"83\" class=\" wp-image-4856 aligncenter\" \/><\/a>\r\n\r\nAlthough this was not previously pointed out, it can be assumed that there is a 1 in the denominator:\r\n\r\nThat is, the density value tells us that we have 19.3 grams for every 1 milliliter of volume, and the 1 is an exact number. When we want to use density to convert from mass to volume, the numerator and denominator of density need to be switched\u2014that is, we must take the <em class=\"emphasis\">reciprocal<\/em> of the density. In so doing, we move not only the units but also the numbers:\r\n\r\n<span class=\"informalequation block\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_4.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_4.png\" alt=\"1\/d = 1mL\/19.3g\" width=\"136\" height=\"71\" class=\" wp-image-4857 aligncenter\" \/><\/a><\/span>\r\n<p id=\"ball-ch02_s05_p26\" class=\"para editable block\">This reciprocal density is still a useful conversion factor, but now the mass unit will cancel and the volume unit will be introduced. Thus, if we want to know the volume of 45.9 g of gold, we would set up the conversion as follows:<\/p>\r\n<span class=\"informalequation block\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_5.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_5.png\" alt=\"45.9 g x 1mL\/19.3g = 2.38 mL\" width=\"259\" height=\"66\" class=\" wp-image-4858 aligncenter\" \/><\/a><\/span>\r\n<p id=\"ball-ch02_s05_p27\" class=\"para editable block\">Note how the mass units cancel, leaving the volume unit, which is what we\u2019re looking for.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Example 2<\/h3>\r\n<p id=\"ball-ch02_s05_p28\" class=\"para\">A cork stopper from a bottle of wine has a mass of 3.78 g. If the density of cork is 0.22 g\/cm<sup class=\"superscript\">3<\/sup>, what is the volume of the cork?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p29\" class=\"para\">To use density as a conversion factor, we need to take the reciprocal so that the mass unit of density is in the denominator. Taking the reciprocal, we find<\/p>\r\n<span class=\"informalequation\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_6.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_6.png\" alt=\"1\/d = 1cm^3\/0.22g\" width=\"135\" height=\"79\" class=\"alignnone wp-image-4859\" \/><\/a><\/span>\r\n<p id=\"ball-ch02_s05_p30\" class=\"para\">We can use this expression as the conversion factor. So<\/p>\r\n<span class=\"informalequation\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_7.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_7.png\" alt=\"3.78 g x 1 cm^3\/0.22g = 17.2 cm^3\" width=\"272\" height=\"72\" class=\"alignnone wp-image-4860\" \/><\/a><\/span>\r\n\r\nThen, taking significant figures into consideration, since the density only has two significant figures, the final answer is 17 cm<sup>3<\/sup>.\r\n\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p31\" class=\"para\">What is the volume of 3.78 g of gold?<\/p>\r\n&nbsp;\r\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\r\n<p id=\"ball-ch02_s05_p32\" class=\"para\">0.196 cm<sup class=\"superscript\">3<\/sup><\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Example 3<\/h3>\r\n<p class=\"Indent\">If a 5.00 g sample has a density of 2.50 g\/mL, what volume does it occupy?<\/p>\r\n&nbsp;\r\n<p class=\"Solution\"><strong>Solution<\/strong><span><strong>\u00a0<\/strong>\u00a0 <\/span><\/p>\r\n<p class=\"Indent\">First, start with what you know: 5.00 g<\/p>\r\n<p class=\"Indent\">Look at the density value as a \u201cconversion factor\u201d (2.50 g\/mL) and arrange it so it CANCELS what you already know. Thus, in this case we must invert it.<\/p>\r\n<p class=\"Indent\">Multiply and cancel units\u2026<\/p>\r\n$latex 5.00\\;\\rule[0.75ex]{1.0em}{0.1ex}\\hspace{-1.0em}\\text{g} \\times \\frac{1\\;\\text{mL}}{2.50\\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{g}} = 2.00\\;\\text{mL} $\r\n\r\n&nbsp;\r\n<p class=\"SelfTest\"><em><strong>Test Yourself<\/strong><\/em><\/p>\r\n<p class=\"Indentpoints\">a)<span>\u00a0\u00a0 <\/span>Isopropyl alcohol has a density of 0.785 g\/mL.\r\nWhat volume should be measured to obtain 10.0 g of the liquid?<\/p>\r\n<p class=\"Indentpoints\">b)<span>\u00a0\u00a0 <\/span>A cube of metal has a mass of 1.45 kg. It is placed in 200.0 mL of water, and the water level rises to 742.1 mL. What is the density of the metal?<\/p>\r\n&nbsp;\r\n\r\n<em><strong>Answers<\/strong><\/em>\r\n\r\na) 12.7 mL \u00a0 \u00a0 \u00a0 \u00a0 \u00a0b) 2.67 g\/mL\r\n\r\n<\/div>\r\nCare must be used with density as a conversion factor. Make sure the mass units are the same, or the volume units are the same, before using density to convert to a different unit. Often, the unit of the given quantity must be first converted to the appropriate unit before applying density as a conversion factor.\r\n<h2>Key Concepts and Summary<\/h2>\r\nDensity relates a substance\u2019s mass and volume.\u00a0Density can be used to calculate volume from a given mass or mass from a given volume.\r\n<div class=\"callout block\" id=\"ball-ch02_s05_n06\">\r\n<div class=\"qandaset block\" id=\"ball-ch02_s05_qs01\">\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Exercises<\/h3>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s05_qs01_p13\" class=\"para\">1. \u00a0Give at least three possible units for density.<\/p>\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">2. \u00a0A sample of iron has a volume of 48.2 cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">. What is its mass?<\/span>\r\n<div class=\"question\">\r\n<p id=\"ball-ch02_s05_qs01_p21\" class=\"para\">3. \u00a0The volume of hydrogen used by the <em class=\"emphasis\">Hindenburg<\/em>, the German airship that exploded in New Jersey in 1937, was 2.000 \u00d7 10<sup class=\"superscript\">8<\/sup> L. If hydrogen gas has a density of 0.0899 g\/L, what mass of hydrogen was used by the airship?<\/p>\r\n\r\n<\/div>\r\n<span style=\"font-size: 1em\">4. \u00a0A typical engagement ring has 0.77 cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\"> of gold. What mass of gold is present?<\/span>\r\n\r\n<span style=\"font-size: 1em\">5. \u00a0What is the volume of 100.0 g of lead if lead has a density of 11.34 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">?<\/span>\r\n\r\n<span style=\"font-size: 1em\">6. \u00a0What is the volume in liters of 222 g of neon if neon has a density of 0.900 g\/L?<\/span>\r\n\r\n<span style=\"font-size: 1em\">7. \u00a0Which has the greater volume, 100.0 g of iron (<\/span><em class=\"emphasis\" style=\"font-size: 1em\">d<\/em><span style=\"font-size: 1em\"> = 7.87 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">) or 75.0 g of gold (<\/span><em class=\"emphasis\" style=\"font-size: 1em\">d<\/em><span style=\"font-size: 1em\"> = 19.3 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">)?<\/span>\r\n\r\n&nbsp;\r\n\r\n<b>Answers<\/b>\r\n\r\n1. \u00a0g\/mL, g\/L, and kg\/L (answers will vary)\r\n\r\n2. \u00a0379 g\r\n\r\n3. \u00a01.80 \u00d7 10<sup class=\"superscript\">7<\/sup> g\r\n\r\n4. \u00a015 g\r\n\r\n5. \u00a08.818 cm<sup class=\"superscript\">3<\/sup>\r\n\r\n6. \u00a0247 L\r\n\r\n7. \u00a0The 100.0 g of iron has the greater volume.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"section\" id=\"ball-ch02_s05\" lang=\"en\">\n<div class=\"learning_objectives editable block\" id=\"ball-ch02_s05_n01\">\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li><span style=\"font-size: 1em\">Define density and use it as a conversion factor.<\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"section\" id=\"ball-ch02_s05\" lang=\"en\">\n<p id=\"ball-ch02_s05_p14\" class=\"para editable block\"><span class=\"margin_term\"><a class=\"glossterm\">Density\u00a0<\/a><\/span>is a physical property that is defined as a substance\u2019s mass divided by its volume:<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\">density =\u00a0mass\/volume\u00a0\u00a0or\u00a0d = m\/V<\/span><\/p>\n<p id=\"ball-ch02_s05_p15\" class=\"para editable block\">Density is usually a measured property of a substance, so its numerical value affects the significant figures in a calculation. Notice that density is defined in terms of two dissimilar units, mass and volume. That means that density overall has derived units, just like velocity. Common units for density include g\/mL, g\/cm<sup class=\"superscript\">3<\/sup>, g\/L, kg\/L, and even kg\/m<sup class=\"superscript\">3<\/sup>. Densities for some common substances are listed in <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 &#8220;Densities of Some Common Substances&#8221;<\/a>.<\/p>\n<div class=\"table block\" id=\"ball-ch02_s05_t01\">\n<p class=\"title\"><strong><span class=\"title-prefix\">Table 1.<\/span><\/strong> Densities of Some Common Substances<\/p>\n<table style=\"border-spacing: 0px\" cellpadding=\"0\">\n<thead>\n<tr>\n<th>Substance<\/th>\n<th>Density (g\/mL or g\/cm<sup class=\"superscript\">3<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>water<\/td>\n<td>1.0<\/td>\n<\/tr>\n<tr>\n<td>gold<\/td>\n<td>19.3<\/td>\n<\/tr>\n<tr>\n<td>mercury<\/td>\n<td>13.6<\/td>\n<\/tr>\n<tr>\n<td>air<\/td>\n<td>0.0012<\/td>\n<\/tr>\n<tr>\n<td>cork<\/td>\n<td>0.22\u20130.26<\/td>\n<\/tr>\n<tr>\n<td>aluminum<\/td>\n<td>2.7<\/td>\n<\/tr>\n<tr>\n<td>iron<\/td>\n<td>7.87<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"ball-ch02_s05_p16\" class=\"para editable block\">Because of how it is defined, density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm<sup class=\"superscript\">3<\/sup>. How can you determine what mass of aluminum you have without measuring it? You can use the volume to calculate it. If you multiply the given volume by the known density (from <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 &#8220;Densities of Some Common Substances&#8221;<\/a>), the volume units will cancel and leave you with mass units, telling you the mass of the sample:<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\"> 7.88\u00a0cm<sup>3<\/sup>\u2009\u00d7\u20092.7\u00a0g\/cm<sup>3\u00a0<\/sup>= 21\u00a0g\u00a0of\u00a0aluminum<\/span><\/p>\n<p id=\"ball-ch02_s05_p17\" class=\"para editable block\">where we have limited our answer to two significant figures.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Example 1<\/h3>\n<p id=\"ball-ch02_s05_p18\" class=\"para\">What is the mass of 44.6 mL of mercury?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\n<p id=\"ball-ch02_s05_p19\" class=\"para\">Use the density from <a class=\"xref\" href=\"#ball-ch02_s05_t01\">Table 1 &#8220;Densities of Some Common Substances&#8221;<\/a> as a conversion factor to go from volume to mass:<\/p>\n<p><span class=\"informalequation\">44.6\u00a0mL\u2009\u00d7\u200913.6\u00a0g\/mL = 607\u00a0g<\/span><\/p>\n<p id=\"ball-ch02_s05_p20\" class=\"para\">The mass of the mercury is 607 g.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\n<p id=\"ball-ch02_s05_p21\" class=\"para\">What is the mass of 25.0 cm<sup class=\"superscript\">3<\/sup> of iron?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\n<p id=\"ball-ch02_s05_p22\" class=\"para\">197 g<\/p>\n<\/div>\n<p id=\"ball-ch02_s05_p23\" class=\"para editable block\">Density can also be used as a conversion factor to convert mass to volume\u2014but care must be taken. We have already demonstrated that the number that goes with density normally goes in the numerator when density is written as a fraction. Take the density of gold, for example:<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_3.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_3.png\" alt=\"d = 19.3 g\/1 mL\" width=\"225\" height=\"83\" class=\"wp-image-4856 aligncenter\" \/><\/a><\/p>\n<p>Although this was not previously pointed out, it can be assumed that there is a 1 in the denominator:<\/p>\n<p>That is, the density value tells us that we have 19.3 grams for every 1 milliliter of volume, and the 1 is an exact number. When we want to use density to convert from mass to volume, the numerator and denominator of density need to be switched\u2014that is, we must take the <em class=\"emphasis\">reciprocal<\/em> of the density. In so doing, we move not only the units but also the numbers:<\/p>\n<p><span class=\"informalequation block\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_4.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_4.png\" alt=\"1\/d = 1mL\/19.3g\" width=\"136\" height=\"71\" class=\"wp-image-4857 aligncenter\" \/><\/a><\/span><\/p>\n<p id=\"ball-ch02_s05_p26\" class=\"para editable block\">This reciprocal density is still a useful conversion factor, but now the mass unit will cancel and the volume unit will be introduced. Thus, if we want to know the volume of 45.9 g of gold, we would set up the conversion as follows:<\/p>\n<p><span class=\"informalequation block\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_5.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_5.png\" alt=\"45.9 g x 1mL\/19.3g = 2.38 mL\" width=\"259\" height=\"66\" class=\"wp-image-4858 aligncenter\" \/><\/a><\/span><\/p>\n<p id=\"ball-ch02_s05_p27\" class=\"para editable block\">Note how the mass units cancel, leaving the volume unit, which is what we\u2019re looking for.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Example 2<\/h3>\n<p id=\"ball-ch02_s05_p28\" class=\"para\">A cork stopper from a bottle of wine has a mass of 3.78 g. If the density of cork is 0.22 g\/cm<sup class=\"superscript\">3<\/sup>, what is the volume of the cork?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong>Solution<\/strong><\/p>\n<p id=\"ball-ch02_s05_p29\" class=\"para\">To use density as a conversion factor, we need to take the reciprocal so that the mass unit of density is in the denominator. Taking the reciprocal, we find<\/p>\n<p><span class=\"informalequation\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_6.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_6.png\" alt=\"1\/d = 1cm^3\/0.22g\" width=\"135\" height=\"79\" class=\"alignnone wp-image-4859\" \/><\/a><\/span><\/p>\n<p id=\"ball-ch02_s05_p30\" class=\"para\">We can use this expression as the conversion factor. So<\/p>\n<p><span class=\"informalequation\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2015\/11\/other_units_7.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/other_units_7.png\" alt=\"3.78 g x 1 cm^3\/0.22g = 17.2 cm^3\" width=\"272\" height=\"72\" class=\"alignnone wp-image-4860\" \/><\/a><\/span><\/p>\n<p>Then, taking significant figures into consideration, since the density only has two significant figures, the final answer is 17 cm<sup>3<\/sup>.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis bolditalic\">Test Yourself<\/em><\/strong><\/p>\n<p id=\"ball-ch02_s05_p31\" class=\"para\">What is the volume of 3.78 g of gold?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"simpara\"><strong><em class=\"emphasis\">Answer<\/em><\/strong><\/p>\n<p id=\"ball-ch02_s05_p32\" class=\"para\">0.196 cm<sup class=\"superscript\">3<\/sup><\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Example 3<\/h3>\n<p class=\"Indent\">If a 5.00 g sample has a density of 2.50 g\/mL, what volume does it occupy?<\/p>\n<p>&nbsp;<\/p>\n<p class=\"Solution\"><strong>Solution<\/strong><span><strong>\u00a0<\/strong>\u00a0 <\/span><\/p>\n<p class=\"Indent\">First, start with what you know: 5.00 g<\/p>\n<p class=\"Indent\">Look at the density value as a \u201cconversion factor\u201d (2.50 g\/mL) and arrange it so it CANCELS what you already know. Thus, in this case we must invert it.<\/p>\n<p class=\"Indent\">Multiply and cancel units\u2026<\/p>\n<p>[latex]5.00\\;\\rule[0.75ex]{1.0em}{0.1ex}\\hspace{-1.0em}\\text{g} \\times \\frac{1\\;\\text{mL}}{2.50\\;\\rule[0.25ex]{0.5em}{0.1ex}\\hspace{-0.5em}\\text{g}} = 2.00\\;\\text{mL}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p class=\"SelfTest\"><em><strong>Test Yourself<\/strong><\/em><\/p>\n<p class=\"Indentpoints\">a)<span>\u00a0\u00a0 <\/span>Isopropyl alcohol has a density of 0.785 g\/mL.<br \/>\nWhat volume should be measured to obtain 10.0 g of the liquid?<\/p>\n<p class=\"Indentpoints\">b)<span>\u00a0\u00a0 <\/span>A cube of metal has a mass of 1.45 kg. It is placed in 200.0 mL of water, and the water level rises to 742.1 mL. What is the density of the metal?<\/p>\n<p>&nbsp;<\/p>\n<p><em><strong>Answers<\/strong><\/em><\/p>\n<p>a) 12.7 mL \u00a0 \u00a0 \u00a0 \u00a0 \u00a0b) 2.67 g\/mL<\/p>\n<\/div>\n<p>Care must be used with density as a conversion factor. Make sure the mass units are the same, or the volume units are the same, before using density to convert to a different unit. Often, the unit of the given quantity must be first converted to the appropriate unit before applying density as a conversion factor.<\/p>\n<h2>Key Concepts and Summary<\/h2>\n<p>Density relates a substance\u2019s mass and volume.\u00a0Density can be used to calculate volume from a given mass or mass from a given volume.<\/p>\n<div class=\"callout block\" id=\"ball-ch02_s05_n06\">\n<div class=\"qandaset block\" id=\"ball-ch02_s05_qs01\">\n<div class=\"bcc-box bcc-info\">\n<h3>Exercises<\/h3>\n<div class=\"question\">\n<p id=\"ball-ch02_s05_qs01_p13\" class=\"para\">1. \u00a0Give at least three possible units for density.<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">2. \u00a0A sample of iron has a volume of 48.2 cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">. What is its mass?<\/span><\/p>\n<div class=\"question\">\n<p id=\"ball-ch02_s05_qs01_p21\" class=\"para\">3. \u00a0The volume of hydrogen used by the <em class=\"emphasis\">Hindenburg<\/em>, the German airship that exploded in New Jersey in 1937, was 2.000 \u00d7 10<sup class=\"superscript\">8<\/sup> L. If hydrogen gas has a density of 0.0899 g\/L, what mass of hydrogen was used by the airship?<\/p>\n<\/div>\n<p><span style=\"font-size: 1em\">4. \u00a0A typical engagement ring has 0.77 cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\"> of gold. What mass of gold is present?<\/span><\/p>\n<p><span style=\"font-size: 1em\">5. \u00a0What is the volume of 100.0 g of lead if lead has a density of 11.34 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">?<\/span><\/p>\n<p><span style=\"font-size: 1em\">6. \u00a0What is the volume in liters of 222 g of neon if neon has a density of 0.900 g\/L?<\/span><\/p>\n<p><span style=\"font-size: 1em\">7. \u00a0Which has the greater volume, 100.0 g of iron (<\/span><em class=\"emphasis\" style=\"font-size: 1em\">d<\/em><span style=\"font-size: 1em\"> = 7.87 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">) or 75.0 g of gold (<\/span><em class=\"emphasis\" style=\"font-size: 1em\">d<\/em><span style=\"font-size: 1em\"> = 19.3 g\/cm<\/span><sup class=\"superscript\">3<\/sup><span style=\"font-size: 1em\">)?<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Answers<\/b><\/p>\n<p>1. \u00a0g\/mL, g\/L, and kg\/L (answers will vary)<\/p>\n<p>2. \u00a0379 g<\/p>\n<p>3. \u00a01.80 \u00d7 10<sup class=\"superscript\">7<\/sup> g<\/p>\n<p>4. \u00a015 g<\/p>\n<p>5. \u00a08.818 cm<sup class=\"superscript\">3<\/sup><\/p>\n<p>6. \u00a0247 L<\/p>\n<p>7. \u00a0The 100.0 g of iron has the greater volume.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":330,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"2.5 Density - Just Another Conversion Factor","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[54],"class_list":["post-2135","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":2084,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/users\/330"}],"version-history":[{"count":18,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2135\/revisions"}],"predecessor-version":[{"id":4925,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2135\/revisions\/4925"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/parts\/2084"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2135\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/media?parent=2135"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapter-type?post=2135"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/contributor?post=2135"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/license?post=2135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}