Question

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

Answer 1

`(8.34"lbs")/"gal"`

Explanation:

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

`g/"mL" xx "??"/"??" = "lbs"/"gal"`

We need a mass conversion unit (`g to "lbs"`) and a volume conversion unit (`"mL" to "gal"`).

`1 "lb" = 454g` or, for our equation, `(1"lb")/(454g)`

Volume will take two steps - `mL to L and then L to gal`

`1 L = 1000mL` and `1gal = 3.785L` Combining them we get:

`1gal = 3.785L xx (1000mL)/L = 3785mL`
`(3785mL)/(1gal)`

NOW we can apply these to our specific example.

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

Answer 2

`=(8.3lb)/(gal)`

Explanation:

1. Need to know the common equivalence statements that usually are printed at the back of the composition notebooks; i.e.,
   `1kg=1000g`
   `1kg=2.205lb`
   `:. 1000g=2.205lb`
   `1L=1000mL`
   `1gal=3.785L`
2. Knowing these facts will also provide you the needed conversion factors to convert the density of water expressed in `(g)/(ml)` to `(lb)/(gal)` as required.
   `a. 1000g=2.205lb`
   `(1000g)/(2.205lb) or color(red)((2.205lb)/(1000g)`

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

`c. 1gal=3.785L`
`(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.,
`=(1cancel(g))/(cancel(ml))xxcolor(red)((2.205lb)/(1000cancel(g)))xxcolor(blue)((1000cancel(mL))/(1cancel(L)))xxcolor(green)((3.785cancel(L))/(1gal))`
`=(8.3lb)/(gal)`