Question

How many grams of glucose would you use to make a $2M$ solution in $1L$? Glucose $=180$

Answer 1

Hint:
-The molarity is the measure of concentration of solute in a solution in terms of number of moles and the volume of the solution.
-The mass of a solute can be determined by using the molarity, and as the number of moles establishes a relationship between the mass of solute and the molar mass of the same solute.

Complete step-by-step answer:
We know that the molarity of a substance is the measure of the concentration of the solute present in the solution. The definition of molarity says that it is the number of moles of the solute particles which are present per unit volume of the solution.

So in the given question some of the values of the quantities are provided to us, let us write all those quantities first. $2M$ is the molarity of the question, which tells us that two moles of solute is present in one litre of solvent, as per the definition of molarity. Also it is provided to us that the volume is one litre. And the molar mass of the solute which is glucose in this case, is said to be $180g$.

The equation to express the term molarity, as per the definition would be,
$M=\dfrac{n}{V}$
Where $M$ represents the molarity of the solution, $n$ signifies the number of moles of solute which is glucose in this case and $V$, represents the volume of the solution in terms of litre.
Now, we are supposed to find out the amount of glucose present in the fixed amount of volume. For that we will first find out the number of moles using the above equation. After substituting the known values we get,
$n=1L\times 2Mu $
Which is two. So, we got that the number of moles of glucose present in this solution is two. We know that the number of moles of any substance can be defined as the mass of solute present per molar mass of the same solute. So, we get,
$2=\dfrac{mass}{180gmo{{l}^{-1}}}$

So now we will multiply the denominator at the right hand side, in order to get the final value of the mass, we get,
\[2\times 180=mass\]
Now, after the multiplication we get,
$mass=360gmo{{l}^{-1}}$
Now after solving this equation, we get the mass of the glucose as, $360gmo{{l}^{-1}}$, which is the desired answer.

Note: The mass of an unknown solution can be calculated if the molarity and the volume is defined or provided in the question. At first we find out the number of moles of the solute by using $M=\dfrac{n}{V}$, which is basically the definition of the molarity. Then we determine the mass of the substance by using the formula of number of moles which is mass per molar mass.