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?

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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?

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Answer 1 · 2018-02-15T21:26:32

$= 45.5 %$ $=45.5%$

Explanation:

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

$% (\frac{w}{w}) = \frac{mass solute}{mass solution}$ $color(red)(%(w/w)=("mass solute")/("mass solution")$

$w h e r e :$ $where:$

${mass solute=mass of dextrose}_{s o l u t e} = 0.5 k g = 500 g$ $"mass solute=mass of dextrose"_(solute)=0.5kg=500g$

$mass solution = m a s s . s o l u t e_{d e x t r o s e} + m a s s . s o l v e n t_{w a t e r}$ $"mass solution"="mass.solute_(dextrose)+mass. solvent_(water)$
$mass solution = 0.5 k g + {mass of solvent}_{w a t e r}$ $"mass solution"=0.5kg+"mass of solvent"_(water)$

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

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

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%

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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?

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