# Question #6e564

Sep 11, 2017

$\text{37,100 g}$

#### Explanation:

For starters, you should know that

$\text{1 L" = 10^3color(white)(.)"mL}$

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 ${\text{0.737 g mL}}^{- 1}$, which means that you get $\text{0.737 g}$ for every $\text{1 mL}$ of gasoline.

This is equivalent to

${\text{0.737 g mL"^(-1) = "0.737 g"/(1color(red)(cancel(color(black)("mL")))) * (10^3 color(red)(cancel(color(black)("mL"))))/"1 L" = "737 g L}}^{- 1}$

So, you know that $\text{1 L}$ of gasoline has a mass of $\text{737 g}$. Use the fact that

$\text{1 US gal = 3.78 L}$

to convert this to grams per gallon

${\text{737 g L"^(-1) = "737 g"/(1color(red)(cancel(color(black)("L")))) * (3.78 color(red)(cancel(color(black)("L"))))/"1 US gal" = "2785.9 g gal}}^{- 1}$

You can thus say that a $\text{13.3-gal}$ tank will hold

$13.3 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{gal"))) * "2785.9 g"/(1color(red)(cancel(color(black)("gal")))) = color(darkgreen)(ul(color(black)("37,100 g}}}}$

The answer is rounded to three sig figs.