document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005270>Question 1005270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solution XRD is one half sulfur acid while QXJ is 3/4 sulfur acid. How many liters of solution QXJ should be added to a liter of solution XRD to obtain a solution that is 3/5 sulfur acid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621697 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WHAT A MATH TEACHER THINKS:<BR>\n" );
document.write( "The volume of a mix of two liquids is the sum of the volumes mixed together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Amount=Volume%2AConcentration ALIGN=MIDDLE  ALT=\"Amount=Volume%2AConcentration\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No need to specify concentration/amount units, because they are self-explanatory.<BR>\n" );
document.write( "So the math teacher would add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%2F3%29=about+0.667 ALIGN=MIDDLE  ALT=\"highlight%282%2F3%29=about+0.667\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of solution QXJ to 1 Liter solution XRD and mix, expecting to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=about1.667L ALIGN=MIDDLE  ALT=\"about1.667L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of solution with a 0.6 concentration.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "WHAT A SCIENTIST THINKS:<BR>\n" );
document.write( "Chemists know that it is important to specify your units.<BR>\n" );
document.write( "When a chemist says a solution is 50% sulfuric acid,<BR>\n" );
document.write( "they usually mean it contains 50 kg sulfuric acid per 100 kg solution.<BR>\n" );
document.write( "If they want to be clearer, they say it is 50%(w/w).<BR>\n" );
document.write( "Biologists tend to describe how the solutions were prepared.<BR>\n" );
document.write( "When you mix together two substances, the mass of the mixture is the sum of the masses of the components.<BR>\n" );
document.write( "The same is not true about volumes.<BR>\n" );
document.write( "Scientists know that, and so do construction workers.<BR>\n" );
document.write( "Any construction worker knows that mixing 1 cubic yard of rocks and 1 cubic yard of fine sand does not yield 2 cubic yards of mixture.<BR>\n" );
document.write( "A chemist knows that mixing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter of a solution with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters of another solution yields a volume usually close to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bx ALIGN=MIDDLE  ALT=\"1%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liters, but not exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bx ALIGN=MIDDLE  ALT=\"1%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and sometimes quite far from exactly that.<BR>\n" );
document.write( "A synthetic chemist and a biologist shrug and say it is probably close enough for their purposes.<BR>\n" );
document.write( "An analytical chemist says that will make my analysis results very wrong.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "IF A BIOLOGIST IS INVOLVED:<BR>\n" );
document.write( "The way the concentrations of those solutions are described,<BR>\n" );
document.write( "maybe those solutions are usually prepared by a biologist,<BR>\n" );
document.write( "who mixes water and concentrated sulfuric acid to make solutions as follows:<BR>\n" );
document.write( "Solution XRD \"half sulfuric acid\" = 1L water + 1L concentrated sulfuric acid;<BR>\n" );
document.write( "Solution QXJ \"3/4 sulfur acid\" = 1L water + 3L concentrated sulfuric acid.<BR>\n" );
document.write( "Maybe that biologist wanted to make more of<BR>\n" );
document.write( "Solution UVW \"3/5 sulfuric acid\" = 2L water + 3L concentrated sulfuric acid.<BR>\n" );
document.write( "The biologist most likely had a bottle of \"concentrated sulfuric acid\" that contained 98g of sulfuric acid per 100g of liquid.<BR>\n" );
document.write( "The label may have stated \"Assay....98.0%, meaning that its concentration was 98.0%(w/w).<BR>\n" );
document.write( "Data in a handbook says that at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > the density of that solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.8361 ALIGN=MIDDLE  ALT=\"1.8361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22kg+%2F+L%22 ALIGN=MIDDLE  ALT=\"%22kg+%2F+L%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution XRD, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0000L=1.0000kg ALIGN=MIDDLE  ALT=\"1.0000L=1.0000kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > water and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0000L=1.8361kg ALIGN=MIDDLE  ALT=\"1.0000L=1.8361kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrated acid, had a total mass of about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0000kg%2B1.8361kg=2.8361kg ALIGN=MIDDLE  ALT=\"1.0000kg%2B1.8361kg=2.8361kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "a total amount of pure acid of about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.98%2A1.8361kg=1.7994kg ALIGN=MIDDLE  ALT=\"0.98%2A1.8361kg=1.7994kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(I say \"about\" because a biologist does not measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1L ALIGN=MIDDLE  ALT=\"1L\"   DISABLED_style= \"max-width:90%; height:auto;\" > volumes with anything near a precision of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0001L ALIGN=MIDDLE  ALT=\"0.0001L\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( "The calculated acid concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.98%2A1.8361kg%2F%222.8361+kg%22=0.634=%2263.4+%25+%7B+w+%2F+w+%29%22 ALIGN=MIDDLE  ALT=\"0.98%2A1.8361kg%2F%222.8361+kg%22=0.634=%2263.4+%25+%7B+w+%2F+w+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The handbook says that the density of that solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5354 ALIGN=MIDDLE  ALT=\"1.5354\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22kg+%2F+L%22 ALIGN=MIDDLE  ALT=\"%22kg+%2F+L%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%220.634+kg++acid%22%2F%221+kg++solution%22%29%281.5354kgsolution%2F%221+L+solution%22%29=0.9741 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kg+acid%2F%22L+solution%22 ALIGN=MIDDLE  ALT=\"kg+acid%2F%22L+solution%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution QXJ, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0000L=1.0000kg ALIGN=MIDDLE  ALT=\"1.0000L=1.0000kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > water and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.0000L=3%2A1.8361kg=5.5083kg ALIGN=MIDDLE  ALT=\"3.0000L=3%2A1.8361kg=5.5083kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrated acid, had a total mass of about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0000kg%2B5.5083kg=6.5083kg ALIGN=MIDDLE  ALT=\"1.0000kg%2B5.5083kg=6.5083kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.98%2A5.5083kg=5.3981kg ALIGN=MIDDLE  ALT=\"0.98%2A5.5083kg=5.3981kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of pure acid.<BR>\n" );
document.write( "The calculated acid concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.3981kgacid%2F%226.5083+kgsolution%22=0.829=82.9%25 ALIGN=MIDDLE  ALT=\"5.3981kgacid%2F%226.5083+kgsolution%22=0.829=82.9%25\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The handbook says that the density of that solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5354 ALIGN=MIDDLE  ALT=\"1.5354\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22kg+%2F+L%22 ALIGN=MIDDLE  ALT=\"%22kg+%2F+L%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%220.829+kg++acid%22%2F%221+kg++solution%22%29%281.7584kgsolution%2F%221+L+solution%22%29=1.4585 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kg+acid%2F%22L+solution%22 ALIGN=MIDDLE  ALT=\"kg+acid%2F%22L+solution%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solution, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.0000L=2.0000kg ALIGN=MIDDLE  ALT=\"2.0000L=2.0000kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > water and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.0000L=3%2A1.8361kg=5.5083kg ALIGN=MIDDLE  ALT=\"3.0000L=3%2A1.8361kg=5.5083kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrated acid, had a total mass of about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.0000kg%2B5.5083kg=7.5083kg ALIGN=MIDDLE  ALT=\"2.0000kg%2B5.5083kg=7.5083kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.98%2A5.5083kg=5.3981kg ALIGN=MIDDLE  ALT=\"0.98%2A5.5083kg=5.3981kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of pure acid.<BR>\n" );
document.write( "The calculated acid concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.3981kgacid%2F%227.5083+kgsolution%22=0.719=71.9%25 ALIGN=MIDDLE  ALT=\"5.3981kgacid%2F%227.5083+kgsolution%22=0.719=71.9%25\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The handbook says that the density of that solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6326 ALIGN=MIDDLE  ALT=\"1.6326\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22kg+%2F+L%22 ALIGN=MIDDLE  ALT=\"%22kg+%2F+L%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.7190kgacid%2F%221+kg++solution%22%29%281.6326kgsolution%2F%221+Lsolution%22%29=1.1738 ALIGN=MIDDLE  ALT=\"%280.7190kgacid%2F%221+kg++solution%22%29%281.6326kgsolution%2F%221+Lsolution%22%29=1.1738\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kg+acid%2F%22L+solution%22 ALIGN=MIDDLE  ALT=\"kg+acid%2F%22L+solution%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Mixing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i.0000L=1.5354kg ALIGN=MIDDLE  ALT=\"i.0000L=1.5354kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of solution XRD,<BR>\n" );
document.write( "containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9741kg ALIGN=MIDDLE  ALT=\"0.9741kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > pure acid and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%282%2F3%29%281.7584kg%29=1.1723kg ALIGN=MIDDLE  ALT=\"L=%282%2F3%29%281.7584kg%29=1.1723kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of Solution QXJ,<BR>\n" );
document.write( "containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%281.4585kg%29=0.9723kg ALIGN=MIDDLE  ALT=\"%282%2F3%29%281.4585kg%29=0.9723kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > pure acid, the biologist gets<BR>\n" );
document.write( "a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9741kg%2B0.9723kg=1.9464kg ALIGN=MIDDLE  ALT=\"0.9741kg%2B0.9723kg=1.9464kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > pure acid in<BR>\n" );
document.write( "a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5354kg%2B1.1723kg=2.7077kg ALIGN=MIDDLE  ALT=\"1.5354kg%2B1.1723kg=2.7077kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of solution.<BR>\n" );
document.write( "The concentration is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.9464%2F2.7077=0.7188 ALIGN=MIDDLE  ALT=\"1.9464%2F2.7077=0.7188\"   DISABLED_style= \"max-width:90%; height:auto;\" > in kg pure acid/kg solution,<BR>\n" );
document.write( "which still rounds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=71.9%25 ALIGN=MIDDLE  ALT=\"71.9%25\"   DISABLED_style= \"max-width:90%; height:auto;\" > , close enough for the biologist.<BR>\n" );
document.write( "The final volume of solution obtained is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.7077kgsolution%281Lsolution%2F1.6326kgsolution%29=1.659L ALIGN=MIDDLE  ALT=\"2.7077kgsolution%281Lsolution%2F1.6326kgsolution%29=1.659L\"   DISABLED_style= \"max-width:90%; height:auto;\" > , also close enough for the biologist.<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF A CHEMIST WAS DESCRIBING THOSE SOLUTIONS:<BR>\n" );
document.write( "When a chemist says a solution is 50% sulfuric acid,<BR>\n" );
document.write( "they usually mean it contains 50 kg sulfuric acid per 100 kg solution.<BR>\n" );
document.write( "If they want to be clearer, they say it is 50%(w/w).<BR>\n" );
document.write( "That is a pretty dense solution;<BR>\n" );
document.write( "At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter has a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.3951 ALIGN=MIDDLE  ALT=\"1.3951\"   DISABLED_style= \"max-width:90%; height:auto;\" > kg.<BR>\n" );
document.write( "When someone says a solution is 60% sulfuric acid,<BR>\n" );
document.write( "they usually mean it contains 60 kg sulfuric acid per 100 kg solution.<BR>\n" );
document.write( "If they want to be clearer, they say it is 60%(w/w).<BR>\n" );
document.write( "That is a denser solution.<BR>\n" );
document.write( "At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter has a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4983 ALIGN=MIDDLE  ALT=\"1.4983\"   DISABLED_style= \"max-width:90%; height:auto;\" > kg.<BR>\n" );
document.write( "When someone says a solution is 75% sulfuric acid,<BR>\n" );
document.write( "they usually mean it contains 75 kg sulfuric acid per 100 kg solution.<BR>\n" );
document.write( "If they want to be clearer, they say it is 75%(w/w).<BR>\n" );
document.write( "That is an even denser solution.<BR>\n" );
document.write( "At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter has a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6692 ALIGN=MIDDLE  ALT=\"1.6692\"   DISABLED_style= \"max-width:90%; height:auto;\" > kg.<BR>\n" );
document.write( "If at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5EoC ALIGN=MIDDLE  ALT=\"20%5EoC\"   DISABLED_style= \"max-width:90%; height:auto;\" > you measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter of 50% sulfuric acid solution,<BR>\n" );
document.write( "with a total mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.3951kg ALIGN=MIDDLE  ALT=\"1.3951kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%281.3951kg%29=0.0.6976kg ALIGN=MIDDLE  ALT=\"0.5%281.3951kg%29=0.0.6976kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > sulfuric acid, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Liter of 75% sulfuric solution with a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%291.6692kg=1.1128kg ALIGN=MIDDLE  ALT=\"%282%2F3%291.6692kg=1.1128kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , containing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75%281.1128kg%29=0.8346kg ALIGN=MIDDLE  ALT=\"0.75%281.1128kg%29=0.8346kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > sulfuric acid, you get<BR>\n" );
document.write( "a total mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.3951kg%2B1.1128kg=2.5079kg ALIGN=MIDDLE  ALT=\"1.3951kg%2B1.1128kg=2.5079kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of solution containing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6976kg%2B0.8346kg=1.5322kg ALIGN=MIDDLE  ALT=\"0.6976kg%2B0.8346kg=1.5322kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of sulfuric acid.<BR>\n" );
document.write( "The concentration of the resulting solution is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5322kg%2F%222.5079+kg%22=0.611%28rounded%29=%2261.1%25%28rounded%29%22 ALIGN=MIDDLE  ALT=\"1.5322kg%2F%222.5079+kg%22=0.611%28rounded%29=%2261.1%25%28rounded%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Looking in a handbook, we find that a solution with that final concentration will have a density of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5102 ALIGN=MIDDLE  ALT=\"1.5102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22kg+%2F+L%22 ALIGN=MIDDLE  ALT=\"%22kg+%2F+L%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5079kg ALIGN=MIDDLE  ALT=\"2.5079kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > of final solution will have a volume of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.5079kg%29%2A%281L%2F%221.5102+kg%22%29=1.661L%28rounded%29 ALIGN=MIDDLE  ALT=\"%282.5079kg%29%2A%281L%2F%221.5102+kg%22%29=1.661L%28rounded%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );