Question

900 ml of ${{H}_{2}}O$ is added to 4 ${W}/{W}\;$% of solution. Calculate resultant $\dfrac{w}{w}$%?

Answer 1

Hint:
Complete step by step solution:
- The concentration of a solution can be expressed in numerous methods such as molality, normality, percent by mass or mass percentage, percent by volume, percent mass by volume etc.
- If a combination of a given ratio or percentage strength is diluted to twice its original quantity, its active ingredient will be contained in twice as several parts of the whole and its strength hence will be reduced by one-half.
- If the quantity of active ingredient remains identical and the volume gets higher, the concentration gets lesser. Similarly, if the amount of active ingredient remains the same and the volume gets reduced, the concentration rises.
- Let the total weight of the solute be 4 gram (since given as 4 ${W}/{W}\;$%) and total weight of solution be 100 gram. After mixing the percentage strength can be found as follows
\[\%w/w\ =\left( \dfrac{4\times 100}{100+900} \right) \%=\dfrac{400}{1000}\%=0.4\%\]

Therefore the resultant $\dfrac{w}{w}$ % is 0.4%.

Note: Keep in mind that the above mentioned relationship is normally true except for volume-in-volume and weight-in volume solutions which contains components which contract when mixed together. It is impossible to add the volume of ingredients and get the total volume of the final product in all cases and it is possible when mixing solids.