Question #6e564

1 Answer
Sep 11, 2017

Answer:

#"37,100 g"#

Explanation:

For starters, you should know that

#"1 L" = 10^3color(white)(.)"mL"#

As you know, the density of a substance tells you the mass of exactly #1# unit of volume of that substance.

In this case, you know that this particular brand of gasoline as a density of #"0.737 g mL"^(-1)#, which means that you get #"0.737 g"# for every #"1 mL"# of gasoline.

This is equivalent to

#"0.737 g mL"^(-1) = "0.737 g"/(1color(red)(cancel(color(black)("mL")))) * (10^3 color(red)(cancel(color(black)("mL"))))/"1 L" = "737 g L"^(-1)#

So, you know that #"1 L"# of gasoline has a mass of #"737 g"#. Use the fact that

#"1 US gal = 3.78 L"#

to convert this to grams per gallon

#"737 g L"^(-1) = "737 g"/(1color(red)(cancel(color(black)("L")))) * (3.78 color(red)(cancel(color(black)("L"))))/"1 US gal" = "2785.9 g gal"^(-1)#

You can thus say that a #"13.3-gal"# tank will hold

#13.3 color(red)(cancel(color(black)("gal"))) * "2785.9 g"/(1color(red)(cancel(color(black)("gal")))) = color(darkgreen)(ul(color(black)("37,100 g")))#

The answer is rounded to three sig figs.