Question

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

Answer 1

Hint: 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.