Question

5.0g of sodium hydroxide (molar mass 40 g/ mol) is dissolved in little quantities of water and the solution is diluted to 100ml. What is the molarity of the resulting solution?
(A). 0.1 mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$
(B). 1.0 mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$
(C). 0.125 mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$
(D). 1.25 mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$

Answer 1

Hint: Molarity is a mostly used concentration term for solutions. To calculate the molarity of any solution the required data is the number of moles of solute and volume of solution.

Complete Step-by-step solution:
The given data is weight of sodium hydroxide - 5g
Molar mass of sodium hydroxide – 40 g/mol
Volume of the solution – 100ml
Molarity is defined as the number of moles of solute present in the unit volume of the solution, usually in liters.
The formula for molarity of a solution ${\text{M = }}\dfrac{{\text{n}}}{{{\text{V}}\left( {{\text{lt}}} \right)}}$ where,
n- number of moles of sodium hydroxide
V- volume of the solution in liters
As the given question mentioned the solution is diluted to 100ml, this means that the solution is in milliliters volume. In order to substitute the volume in milliliters during the molarity calculation, volume in liters has to be converted to milliliters.
Conversion of liters to milliliters-
1000 milliliters = 1 liters
1millilitres = $\dfrac{1}{{1000}}$liters
Therefore the volume of the solution in the formula of molarity has to be replaced by $\dfrac{{{\text{1000}}}}{{{\text{V}}\left( {{\text{ml}}} \right)}}$.
Since the formula for number of moles is, weight of the substance divided by molecular weight${\text{n = }}\dfrac{{\text{w}}}{{{\text{GMW}}}}$.
Substituting the weight of NaOH (w), molar mass (GMW), volume in the formula for molarity\begin{gathered}
{\text{M = }}\dfrac{{{{5 \times 1000}}}}{{{{40 \times 100}}}} \\
{\text{M = }}\dfrac{{\text{5}}}{{\text{4}}} \\
\end{gathered}
M = 1.25 mol/lt.
Therefore the molarity of the resulting solution is 1.25 mol /lt.

The answer for the above question is option (D)1.25 mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$.

Note: The answer in the options is given with the units as moles per decimeter cube. 1 cubic decimeter equals to 1000 milliliters or 1 liter. So if the answer mentions mol ${\text{l}}{{\text{t}}^{{\text{ - 1}}}}$ or mol ${\text{d}}{{\text{m}}^{{\text{ - 3}}}}$ both are correct notations for molarity.