Question

An aqueous solution contains $30\% w/v$ of urea, density of solution is $1.2g/ml$ . Calculate the mass of water in $100ml$ solution.

Answer 1

We can calculate the mass of water is calculated using the mass of the solution and mass of urea. We can use the density of the solution and volume of the solution to calculate the mass of the solution. The product of the density of the solution and volume of the solution is the mass of the solution.
We know that the formula of density of the solution is,
${\text{Density of the solution}} = \dfrac{{{\text{Mass of the solution}}}}{{{\text{Volume of the solution}}}}$.

Complete step by step answer:
Given,
Weight/volume of urea is $30\% w/v$.
Density of the solution is $1.2g/ml$.
Mass of solution is $100ml$.
Weight/volume of urea is $30\% w/v$ means 30grams of urea is present in aqueous solution in $100ml$ of solution.
We know that the formula of density of the solution is,
${\text{Density of the solution}} = \dfrac{{{\text{Mass of the solution}}}}{{{\text{Volume of the solution}}}}$
We can rearrange the density of the solution to get the mass of the solution.
${\text{Mass of the solution}} = {\text{Density of the solution}} \times {\text{Volume of the solution}}$
The values of the density of the solution and volume of the solution are substituted in the formula to the mass of the solution.
${\text{Mass of the solution}} = {\text{Density of the solution}} \times {\text{Volume of the solution}}$
Mass of the solution $= 1.2\dfrac{g}{{ml}} \times 100ml$
Mass of the solution $= 120g$
We have calculated the mass of the solution is $120g$.
We know the mass of the solution is the sum of the mass of the solute and mass of the solvent.
${\text{Mass of the solution}} = {\text{Mass of the solute}} + {\text{Mass of the solvent}}$
We can rearrange the formula of mass of the solution to get the mass of the solvent.
${\text{Mass of the solvent}} = {\text{Mass of the solution}} - {\text{Mass of the solute}}$
The mass of the solute is the mass of the urea.
The mass of the solvent is the mass of the water.
Mass of the urea is 30grams. Mass of the solution is 120grams.
Let us substitute the mass of urea and mass of solution to get the mass of water.
${\text{Mass of the water}} = {\text{Mass of the solution}} - {\text{Mass of the urea}}$
Mass of water $= 120g - 30g$
Mass of water $= 90g$

So, mass of water in 100ml of solution is $90g$.

Note: We can calculate the mass of solution using the weight/volume percent of the solution.
For example, the grams of glucose that a patient receives have to be given.
Given,
Volume of the solution = $750mL$
Weight/volume percent =$10\% \left( {w/v} \right)$
The mass of the glucose is calculated as,
$\left( {\dfrac{w}{v}} \right)\% = \dfrac{{{\text{Mass of solute}}\left( g \right)}}{{{\text{Volume of solution}}\left( {mL} \right)}} \times 100\%$
$10\% = \dfrac{x}{{750mL}} \times 100\%$
$x = 750mL{\text{ solution}} \times \dfrac{{10g{\text{ glucose}}}}{{100mL{\text{ solution}}}}$
$x = 75g$
The grams of glucose that a patient receives is $75g$.