Question

The density of a salt solution is $1.13gc{{m}^{-3}}$ and it contains $18$of NaCl by weight. The volume of the solution containing $36.0$g of the salt will be
A. $200c{{m}^{3}}$
B. $217c{{m}^{3}}$
C. $177c{{m}^{3}}$
D. $157c{{m}^{3}}$

Answer 1

$18$ of NaCl by weight means $18gm$ of NaCl in $100ml of solution. By knowing the given quantities in the question like volume, density and mass etc. we can calculate the solution.

Complete step by step answer:
Density is the given mass of the substance by the volume of the solution that is
$density=\dfrac{mass}{volume}$
We can change the formula according to the required quantities given in the question.
Mass by mass percentage means mass of the solute by mass of solution. Mass by volume percent means mass of the solute by mass of solution. Volume by volume percent means volume of solute by volume of the solution. Volume by mass percent means volume of the solute by mass of the solution.
Depending on the question the units and calculations can vary. Also, we can convert from one unit to another if required.
Be careful in the question and don’t confuse the two mass quantities and look for the solution properly.
Let the mass of the salt solution be x gm
Given, $18$ of x $=36.0gm$
Therefore,
$\begin{aligned} & \dfrac{18}{100}\times x=36 \\\ & x=\dfrac{36}{\dfrac{18}{100}} \\\ & x=\dfrac{36\times 100}{18} \\\ & x=200gm \\\ \end{aligned}$
Now,

& Density=\dfrac{mass}{volume} \\\ & 1.13=\dfrac{200}{volume} \\\ & Volume=\dfrac{200}{1.13} \\\ & Vol=177c{{m}^{3}} \\\ \end{aligned}$$ **Hence, the volume of the solution is $177c{{m}^{3}}$ option C is correct.** **Note:** You can directly calculate the volume of the given solution in one step to ease the calculations. For that directly take x and put in the second step in which we are calculating the volume of the given solution.