Question

How would you prepare a 0.2M NaOH solution with a volume of 200 ml, form a 0.12M NaOH solution with a volume of 200 ml?

Answer 1

Hint: To solve this question, first we have to understand the term molarity and molarity. Molarity is represented by capital “M” and molality is represented by small “m”.

Complete answer:
Molar solution is also known as molarity. Molarity is one of the standard expressions of solution concentration. The molar solution used the gram molecular weight of a solute in calculating molar concentration present in per litre of the solution. Molarity is denoted by the symbol M. The formula of molarity is given below:
molarity = $\dfrac{\text{moles of solute}}{liters\text{ of solution}}$
the volume of the target solution is 200 mL and the molarity of 0.2 M. concentration will be:
\[\begin{align}
  & C=\dfrac{n}{V} \\
 & {{n}_{NaOH}}=0.2\dfrac{moles}{L}{{.200.10}^{-3}}L \\
 & =0.04\text{ moles NaOH} \\
\end{align}\]
Volume of the stock solution
\[\begin{align}
  & C=\dfrac{n}{V} \\
 & {{V}_{stock}}=\dfrac{0.04moles}{0.12\dfrac{moles}{L}} \\
 & =0.333L=333mL \\
\end{align}\]
Number of moles of stock solution
\[\begin{align}
  & {{n}_{stock}}=C.V=0.12\dfrac{moles}{L}{{.200.10}^{-3}}L \\
 & =0.024moles\text{ NaOH} \\
 & {{\text{n}}_{add}}={{n}_{t\arg et}}-{{n}_{stock}} \\
 & {{n}_{add}}=0.04-0.024=0.016moles \\
\end{align}\]
How many grams require this much moles:
\[0.016moles.\dfrac{40g}{1mole}=0.64g\]

Note:
The mole is a measurement or it is the basic unit which helps to calculate the amount of substance present in the given sample. 1 mole=$6.022X{{10}^{23}}$ particle or atoms or molecules or electrons or protons etc. The number of the constituent particles of atoms such as molecules or atoms or ions present in a given sample is related with the mass of the substance present in the sample using Avogadro's number. We can also derive a relationship between molality and molarity, but calculation of that expression also requires the density of the solution. To calculate molality from molarity we will require the density of the given substance. If the density is given then it is easy to calculate molality from molarity