document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982448>Question 982448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how much water is to be evaporated from 20 liters of 20 percent sugar solution to get 30 percent sugar solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603285 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=603285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the kind of problem that makes a chemist cry (or at least hate the fact that math teacher have little knowledge of or respect for science).\r<BR>\n" );
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document.write( "THE WRONG SOLUTION THAT A MATH TEACHER EXPECTS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= volume of water evaporated, in L.<BR>\n" );
document.write( "The amount of sucrose in each solution is calculated by multiplying concentration times volume;<BR>\n" );
document.write( "concentration used is the percentage expressed as a decimal (0.2 for 20% and 0.3 for 30%),<BR>\n" );
document.write( "and the teacher does not care what units the amount of sucrose is measured in.<BR>\n" );
document.write( "So, the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A0.2=%2820-x%29%2A0.3 ALIGN=MIDDLE  ALT=\"20%2A0.2=%2820-x%29%2A0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A0.2=%2820-x%29%2A0.3 ALIGN=MIDDLE  ALT=\"20%2A0.2=%2820-x%29%2A0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=6-0.3x ALIGN=MIDDLE  ALT=\"4=6-0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-6=-0.3x ALIGN=MIDDLE  ALT=\"4-6=-0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=-0.3x ALIGN=MIDDLE  ALT=\"-2=-0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F%28-0.3%29=x ALIGN=MIDDLE  ALT=\"%28-2%29%2F%28-0.3%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6.67%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "THE SCIENTIST\"S (OR CHEMICAL ENGINEER'S)POINT OF VIEW:<BR>\n" );
document.write( "When solution concentrations are given as percentage,<BR>\n" );
document.write( "especially if it is some solid substance dissolved in water,<BR>\n" );
document.write( "you would want to specify if you meant<BR>\n" );
document.write( "20 grams in a total mass of 100 grams of solution, which you write as 20%(w/w),<BR>\n" );
document.write( "or 20 grams in a total volume of 100 milliliters of solution, which you write as 20%(w/v),<BR>\n" );
document.write( "where the \"w\" and the \"v\" refer to weight and volume respectively.<BR>\n" );
document.write( "We read {w/w) as \"weight in weight\" and (w/v) as \"weight in volume\".\r<BR>\n" );
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document.write( "If someone tells me a sucrose solution's concentration is 20%,<BR>\n" );
document.write( "I would assume it is 20%(w/v), with 20 g sucrose per 100 mL (100 milliliters) of solution,<BR>\n" );
document.write( "and I would go to a table to find that it has a density of 1.0810 g/mL.<BR>\n" );
document.write( "That means that the 100 mL of solution really have a mass of 108.1 grams,<BR>\n" );
document.write( "which would make the concentration<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20g%2F%22108.1+g%22=0.185 ALIGN=MIDDLE  ALT=\"20g%2F%22108.1+g%22=0.185\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 18.5%(w/w).\r<BR>\n" );
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document.write( "A 30%(w/v) sucrose solution, with 30 g sucrose per 100 mL<BR>\n" );
document.write( "has a density of 1.1270g/mL,<BR>\n" );
document.write( "meaning that the weight ratio of sucrose to solution is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30g%2F%22112.7+g%22=0.266 ALIGN=MIDDLE  ALT=\"30g%2F%22112.7+g%22=0.266\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 26.6%(w/w).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20L ALIGN=MIDDLE  ALT=\"20L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of 20%(w/v) sucrose solution have a mass of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820L%29%2A%28%221.081+kg+%2F+L%22%29=21.62kg ALIGN=MIDDLE  ALT=\"%2820L%29%2A%28%221.081+kg+%2F+L%22%29=21.62kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <BR>\n" );
document.write( "and would contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820L%29%2A%28%2220+kg+%2F+100+L%22%29=4kg ALIGN=MIDDLE  ALT=\"%2820L%29%2A%28%2220+kg+%2F+100+L%22%29=4kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > sucrose.\r<BR>\n" );
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document.write( "If <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 30%(w/v) sucrose solution were to contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+kg ALIGN=MIDDLE  ALT=\"4+kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > sucrose, we would have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%2830%2F100%29=4 ALIGN=MIDDLE  ALT=\"x%2A%2830%2F100%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3x=4 ALIGN=MIDDLE  ALT=\"0.3x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F0.3 ALIGN=MIDDLE  ALT=\"x=4%2F0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13.333 ALIGN=MIDDLE  ALT=\"x=13.333\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded),<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.333L ALIGN=MIDDLE  ALT=\"13.333L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of 30%(w/v) sucrose solution have a mass of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813.333L%29%2A%28%221.127+kg+%2F+L%22%29=15.03kg ALIGN=MIDDLE  ALT=\"%2813.333L%29%2A%28%221.127+kg+%2F+L%22%29=15.03kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).\r<BR>\n" );
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document.write( "To get to a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.03kg ALIGN=MIDDLE  ALT=\"15.03kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > from a mass of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.62kg ALIGN=MIDDLE  ALT=\"21.62kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we would need to lose<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.62kg-15.03kg=6.59kg ALIGN=MIDDLE  ALT=\"21.62kg-15.03kg=6.59kg\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and since the lost mass is water,<BR>\n" );
document.write( "with an approximate density of 1.000kg/L = 1.000g/mL,<BR>\n" );
document.write( "the amount of water that needs to be evaporated is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.59L ALIGN=MIDDLE  ALT=\"6.59L\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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