Question

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

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  = $\frac{mass}{volume}$

Now solve for the volume of sucrose;

                  1.12g/mL = $\frac{5}{Volume}$

       Volume  = $\frac{5}{1.12}$    =  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 $\frac{100}{12}$   = 0.037L

Volume of cane juice is  0.037L