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?

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%