Question

How many grams of ${\text{NaOH}}$ are contained in 200 ml of a 0.400M solution?

Answer 1

Using the given molarity and volume of solution calculate the moles of ${\text{NaOH}}$. Determine the molar mass of ${\text{NaOH}}$. Using the moles and molar mass of ${\text{NaOH}}$ calculate the mass of ${\text{NaOH}}$.

Formula Used:
${\text{Molarity = }}\dfrac{{{\text{moles of solute}}}}{{{\text{Liter of Solution}}}}$
${\text{Moles = }}\dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$

Complete step by step answer:
We have to calculate the mass of ${\text{NaOH}}$ in 200 ml of a 0.400M solution.
Using the given molar concentration and volume of ${\text{Molarity = }}\dfrac{{{\text{moles of solute}}}}{{{\text{Liter of Solution}}}}$ the solution we can calculate the moles of ${\text{NaOH}}$ as follows:
Mathematical equation related to molarity, moles and liter of solution is as follows:
$\Rightarrow {\text{Molarity = }}\dfrac{{{\text{moles of solute}}}}{{{\text{Liter of Solution}}}}$

So, to calculate the moles of ${\text{NaOH}}$ we will convert a given volume of solution from ml to L as follows:
We know, 1L = 1000ml
So, $200{\text{ ml }} \times \dfrac{{1{\text{ L}}}}{{{\text{1000 ml }}}} = 0.2{\text{L}}$
Now, substitute 0.400M for molarity, 0.2L for the volume of solution and calculate the moles of ${\text{NaOH}}$.
$\Rightarrow {\text{moles of NaOH = Molarity }} \times {\text{ Liter of solution }}$
$\Rightarrow {\text{moles of NaOH = }}0.400{\text{M}} \times {\text{ 0}}{\text{.2L}}$
$\Rightarrow {\text{moles of NaOH = }}0.08{\text{ moles}}$

Now, we can convert these calculated moles of ${\text{NaOH}}$ to mass as follows:
The mathematical equation related to moles, mass and molar mass is as follows:
$\Rightarrow {\text{Moles = }}\dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$

We can rearrange this equation for mass as follows:
$\Rightarrow {\text{Mass = Moles }} \times {\text{ Molar mass}}$
The molar mass of ${\text{NaOH}}$ = $40.0{\text{ g/mol}}$

Now, substitute 0.08 mol for moles of ${\text{NaOH}}$ , $40.0{\text{ g/mol}}$ for molar mass of ${\text{NaOH}}$ and calculate the mass of ${\text{NaOH}}$.
$\Rightarrow {\text{Mass = 0}}{\text{.08 mol }} \times {\text{ 40}}{\text{.0 g/mol = 3}}{\text{.2 g}}$
Thus, we can say that 3.2 g of ${\text{NaOH}}$ are contained in 200 ml of a 0.400M solution.

Note: Solution is a mixture of solute and solvent. In solution, the solute is the substance that is present in less amount while the solvent is the substance that is present in a large amount. Mostly water is used as a solvent to prepare the solution. Here ${\text{NaOH}}$ is the solute. Molarity is one of the units of concentration.