# 9. The density of water is 1.0 g/mL. What is the density of water in pounds/gallon?

Dec 24, 2017

(8.34"lbs")/"gal"

#### Explanation:

Use "Dimensional Analysis" to determine what "conversion factors" you will need before you do the math.

$\frac{g}{\text{mL" xx "??"/"??" = "lbs"/"gal}}$

We need a mass conversion unit ($g \to \text{lbs}$) and a volume conversion unit ($\text{mL" to "gal}$).

$1 \text{lb} = 454 g$ or, for our equation, $\frac{1 \text{lb}}{454 g}$

Volume will take two steps - $m L \to L \mathmr{and} t h e n L \to g a l$

$1 L = 1000 m L$ and $1 g a l = 3.785 L$ Combining them we get:

$1 g a l = 3.785 L \times \frac{1000 m L}{L} = 3785 m L$
$\frac{3785 m L}{1 g a l}$

NOW we can apply these to our specific example.

(1.0 g)/(mL) xx (1"lb")/(454g) xx (3785mL)/(1gal) = (8.34"lbs")/"gal"

Dec 25, 2017

$= \frac{8.3 l b}{g a l}$

#### Explanation:

1. Need to know the common equivalence statements that usually are printed at the back of the composition notebooks; i.e.,
$1 k g = 1000 g$
$1 k g = 2.205 l b$
$\therefore 1000 g = 2.205 l b$
$1 L = 1000 m L$
$1 g a l = 3.785 L$
2. Knowing these facts will also provide you the needed conversion factors to convert the density of water expressed in $\frac{g}{m l}$ to $\frac{l b}{g a l}$ as required.
$a . 1000 g = 2.205 l b$
(1000g)/(2.205lb) or color(red)((2.205lb)/(1000g)

$b . 1 L = 1000 m L$
(1L)/(1000mL) or color(blue)((1000mL)/(1L)

$c . 1 g a l = 3.785 L$
(1gal)/(3.785L) or color(green)((3.785L)/(1gal)
3. Either of the reflected values are the possible conversion factors, but careful analysis should be taken so that the desired units are obtained; i.e.,
$= \frac{1 \cancel{g}}{\cancel{m l}} \times \textcolor{red}{\frac{2.205 l b}{1000 \cancel{g}}} \times \textcolor{b l u e}{\frac{1000 \cancel{m L}}{1 \cancel{L}}} \times \textcolor{g r e e n}{\frac{3.785 \cancel{L}}{1 g a l}}$
$= \frac{8.3 l b}{g a l}$