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

2 Answers
Dec 24, 2017

Answer:

#(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"#

Dec 25, 2017

Answer:

#=(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)#