Question

Which of the following solutions have the same concentration?
A.$20g$ of $NaOH$ in $200ml$ of solution
B.$0.5mol$ of $NaOH$ in $200ml$ of solution
C.$0.25mol$ of $NaOH$ in $100ml$ of solution
D.$28g$ of $KOH$ in $200ml$ of solution

Answer 1

During this, we can notice and compare the molarity or the concentration of the answer. If the molarity or the concentration is equal then we can conclude that the solutions have a similar concentration.
Formula used:
Concentration of solution $M = \dfrac{{moles}}{{Volume(L)}}$

Complete step by step answer:
Here we are going to take into account all the solutions given within the choices one by one and calculate the concentration. It is defined as the ratio of the number of moles of solute to the volume of solution in liters. Therefore, let’s take into account the solutions one by one with the given quantities.

Option (A). Here first we will calculate the number of moles $NaOH$ using the formula for the number of moles, $n = \dfrac{w}{M}$. Where $w$ is the given mass and $M$ is the molar mass. So we have, $w = 20g,{M_{NaOH}} = 23 + 16 + 1 = 40g/mol$. So $n = \dfrac{{20}}{{40}} = 0.5mole$. Now for molarity we have $n = 0.5mole,V = 0.2L$. Substitute the value in the formula we get,
$M = \dfrac{n}{V} = \dfrac{{0.5}}{{0.2}} = 2.5M$
Option (B). The molarity can be calculated as $M = \dfrac{n}{V} = \dfrac{{0.5}}{{0.2}} = 2.5M$
Option (C). Here we have $n = 0.25mole,V = 0.1L$. So molarity will be $M = \dfrac{n}{V} = \dfrac{{0.25}}{{0.1}} = 2.5M$.
Option (D. First, we will calculate the number of moles $KOH$using the formula for the number of moles, $n = \dfrac{w}{M}$. Where $w$ is the given mass and $M$is the molar mass. So we have, $w = 28g,{M_{KOH}} = 39 + 16 + 1 = 56g/mol$. So $n = \dfrac{{28}}{{56}} = 0.5mole$. Now for molarity we have $n = 0.5mole,V = 0.2L$. Substitute the value in the formula we get,
$M = \dfrac{n}{V} = \dfrac{{0.5}}{{0.2}} = 2.5M$.
The calculated molar concentration of all the solution is $2.5M$.
Therefore, the proper choices are (A),(B),(C) and (D).

Note:
We can express the concentration in different ways. Mass percentage and mole fraction also represent the concentration of the solution. By comparing only the number of moles we cannot conclude that solutions have similar concentrations.