Question

Question #6e564

Answer 1

`"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.