Question

Which of the following solutions is more concentrated in each pair?
${\text{I}}$ : $0.500{\text{ M KCl}}$ or 0.500{\text{ wt % KCl}} in water.
${\text{II}}$ : $1.75{\text{ M}}$ glucose or $1.75{\text{ m}}$ glucose in water.

| ${\text{I}}$ | ${\text{II}}$
---|---|---
(a)| $0.500{\text{ M KCl}}$ | $1.75{\text{ M}}$ glucose
(b)| 0.500{\text{ wt % KCl}} | $1.75{\text{ M}}$ glucose
(c)| $0.500{\text{ M KCl}}$ | $1.75{\text{ m}}$ glucose
(d)| 0.500{\text{ wt % KCl}} | $1.75{\text{ m}}$ glucose

Answer 1

Hint : The solution containing more solute is said to be more concentrated. To solve the given question, find the amount of solute present in the solution in each case. Remember that the molarity of a solution is defined as the number of moles solute present in one liter of given solution.
$n = \dfrac{{{\text{weight of substance}}}}{{{\text{molecular weight of substance}}}}$
Where $n$ is the number of moles.

Complete Step By Step Answer:
A solution is said to be concentrated if it contains more solute.
Consider $0.500{\text{ M KCl}}$ and 0.500{\text{ wt % KCl}} :
Molarity of a solution is defined as the number of moles of solute per liter of solution. $0.500{\text{ M KCl}}$ means $0.5$ moles of ${\text{KCl}}$ are present in one liter of solution.
We know that the number of moles is the ratio of weight of the given substance by the molecular ${\text{weight of KCl = }}$ weight of that substance.
$\Rightarrow$ $n = \dfrac{{{\text{weight of substance}}}}{{{\text{molecular weight of substance}}}}$
We have $n = 0.5$ and the molecular weight of ${\text{KCl}}$ is $39 + 35.5 = 74.5{\text{ g}}$
So, $0.5 \times 74.5 = 37.25{\text{ g}}$
Therefore, $0.500{\text{ M KCl = 37}}{\text{.25 g of KCl}}$ in one liter of solution.
{\text{wt % }} is weight percent. 0.500{\text{ wt % KCl}} means, there is $0.5{\text{ g}}$ of ${\text{KCl}}$ for every $100{\text{ ml}}$ of water.
So, in $1000{\text{ ml}}$ of water $\dfrac{{0.5 \times 1000}}{{100}} = 5{\text{ g}}$ of ${\text{KCl}}$ is present.
Therefore, 0.500{\text{ wt % KCl = 5 g of KCl}} in one liter of solution.
Therefore, $0.500{\text{ M KCl}}$ is more concentrated than 0.500{\text{ wt % KCl}}
Consider $1.75{\text{ M}}$ glucose and $1.75{\text{ m}}$ glucose:
A molar solution is where one mole of solute is dissolved in one liter of final solution. As the solute must contribute some volume to the final solution to get one molar solution, we will need less than $1000{\text{ ml}}$ of water.
A molal solution is one where one mole of solute is dissolved in $1000{\text{ ml}}$ of water. The volume of the solution will be greater than one liter.
From the above points, we can say that, in the case of molar solution the solute is dissolved in less amount of water than in molal solution. This means the molar solution will have higher concentration.
Therefore, $1.75{\text{ M}}$ glucose is more concentrated.
Therefore, option A is the correct answer.

Note :
To solve the first part of this question, we can use the concept of mole. But the second part of the question requires logical thinking. Remember that in the case of a molar solution the solute is dissolved in less amount of water than in molal solution.