Question

How many moles are present in a 4.25 m aqueous solution prepared with 400 g of water?

Answer 1

Use the formula of molality and rearrange the equation, substitute data given in the question to find the number of moles.

Complete answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question. We have been provided with the molarity of the solution, and also with the mass of solvent, which is 400 grams.
So, we will find out the relation of moles and molarity. Now, we know that the formula of molarity is:
$Molarity=\dfrac{given\,mass}{molar\,mass}\times \dfrac{1000}{vol\,of\,sol}$
As we know that the ratio of the given mass and the molar mass is also known as the number of moles. Taking this into account, the formula of molarity can be written as:
$Molarity=\dfrac{moles\,of\,solute}{kg\,of\,solvent}$
Now, we have been given with the molarity and the kilogram of solvent. On rearranging the equation, we have:

& no\,of\,moles=Molarity\times kg\,of\,solvent \\\ & \Rightarrow no\,of\,moles=4.25mol\,k{{g}^{-1}}\times 0.400kg \\\ & \Rightarrow no\,of\,moles=1.70mol \\\ \end{aligned}$$ So, in a 4.25m aqueous solution which is prepared with 400 grams of water, 1.70 moles of the solute are present. **Note:** It is to be noted that in case the temperature of the solution is changed, then it will have no effect on the molality of the solution. The number of moles will also remain the same.