Question

How many liters of cane juice is needed to supply 5g sucrose if cane juice contains 12% sucrose

by mass and has a density of 1.12 g/mL?

Answer 1

Given parameters:

Mass of sucrose = 5g

Density of sucrose = 1.12g/mL

Percentage of sucrose per liter of cane juice = 12%

Unknown:

Volume of cane juice needed = ?

We need to establish the volume - density relationship. Density is the mass of a substance per unit volume.

Mathematically;

Density =
`(mass)/(volume)`

Now solve for the volume of sucrose;

1.12g/mL =
`(5)/(Volume)`

Volume =
`(5)/(1.12)` = 4.46mL = 4.46 x 10⁻³L since 1000mL = 1L

Since 12% of 1 liter of cane juice is sucrose;

12% of x liter of cane juice = 4.46 x 10⁻³L

Volume of cane juice = 4.46 x 10⁻³ x
`(100)/(12)` = 0.037L

Volume of cane juice is 0.037L