Question

If 0,5kg of dextrose is dissolved in 600ml of water to produce a solution with a final volumeof 1000ml what is the percentage w/w strength of the solution?

Answer 1

`=45.5%`

Explanation:

Since the problem calls for the concentration of the solution in %(ww); the suitable formula to solve it is the following:

`color(red)(%(w/w)=("mass solute")/("mass solution")`

`where:`

`"mass solute=mass of dextrose"_(solute)=0.5kg=500g`

`"mass solution"="mass.solute_(dextrose)+mass. solvent_(water)`
`"mass solution"=0.5kg+"mass of solvent"_(water)`

But, given the volume of water and on the assumption that the density of water @`4^oC=1"g/ml"=1"kg/L"`, the mass of the solvent (water) can be obtained as shown below.

`"mass "=("density")("volume")`
`"mass solvent"_(water)=((1kg)/cancel(L)) (600cancel(mL)xx(1cancel(L))/(1000cancel(mL)))`
`"mass"=0.6kg`

This time, masses composing the solution are already known; thus,

`"mass solution=mass solute+mass solvent"`

`"mass solution=mass dextrose+mass water"`

`"mass solution"=0.5kg+0.6kg`

`"mass solution"=1.1kg`

Therefore:

`1.1kg " final mass solution"-=1L " final volume solution"`
or
`1100g " final mass solution"-=1000mL " final volume solution"`
`rho " solution"=(1.1g)/(mL)=(1.1kg)/(L)`

Using the formula highlighted above, the concentration of the solution is:

`color(red)(%(w/w)=("mass solute")/("mass solution")xx100`
`color(red)(%(w/w)=(0.5cancel(kg))/(1.1cancel(kg))xx100`
`color(red)(%(w/w)=0.4545xx100`
`color(red)(%(w/w)=45.5%`

Therefore; the concentration of the solution is 45.5%