Question

Calculate the molarity of a solution containing $20.7\;{\rm{g}}$ of potassium carbonate dissolved in ${\rm{500}}\;{\rm{mL}}$ of solution (assume density of solution $ = 1\;{\rm{g}}{\rm{.m}}{{\rm{L}}^{ - 1}}$).
A. \[{\rm{0}}{\rm{.113}}\;{\rm{M}}\]
B. \[{\rm{0}}{\rm{.213}}\;{\rm{M}}\]
C. \[{\rm{0}}{\rm{.300}}\;{\rm{M}}\]
D. \[{\rm{0}}{\rm{.413}}\;{\rm{M}}\]

Answer 1

Hint: We know that the constituents’ mole can be calculated by the utilization of molar mass and their respective mass which is given.

Complete answer: or Complete step by step answer:
Given, the mass of potassium carbonate is $20.7\;{\rm{g}}$.
The volume of the solution is ${\rm{500}}\;{\rm{mL}}$.
The density of the solution is $1\;{\rm{g}}{\rm{.m}}{{\rm{L}}^{ - 1}}$.
The molar mass of potassium carbonate is ${\rm{138}}\;{\rm{g/mol}}$.
The number of moles of potassium carbonate can be calculated by using the formula is shown below.
${\rm{n}} = \dfrac{{\rm{m}}}{{\rm{M}}}$
Where, n is the number of moles of potassium carbonate, M is the molar mass of potassium carbonate and m is the mass of potassium carbonate.
Substitute all the respective values in the above equation.
$\begin{array}{c}
{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} = \dfrac{{{\rm{20}}{\rm{.7}}\;{\rm{g}}}}{{{\rm{138}}\;{\rm{g/mol}}}}\\
 = 0.15\;{\rm{mol}}
\end{array}$
The number of moles of potassium carbonate are $0.15\;{\rm{mol}}$.
The conversion of volume of solution from milliliters to liters is done as follows.
$\begin{array}{c}
{\rm{1}}\;{\rm{mL}} = 0.001\;{\rm{L}}\\
{\rm{500}}\;{\rm{mL}} = 500 \times 0.001\;{\rm{L}}\\
 = 0.5\;{\rm{L}}
\end{array}$
The molarity of the solution can be calculated by using the formula given below.
${\rm{Molarity}} = \dfrac{{\rm{n}}}{{\rm{V}}}$
Where, n is the number of moles, and V is the volume of the solution.
Substitute all the respective values in the above equation.
$\begin{array}{c}
{\rm{Molarity}} = \dfrac{{{\rm{0}}{\rm{.15}}\;{\rm{mol}}}}{{0.5\;{\rm{L}}}}\\
 = 0.3\;\dfrac{{{\rm{mol}}}}{{\rm{L}}}\\
 = {\rm{0}}{\rm{.3}}\;{\rm{M}}
\end{array}$
Thus, the molarity of the solution containing $20.7\;{\rm{g}}$ of potassium carbonate dissolved in ${\rm{500}}\;{\rm{mL}}$ of solution is ${\rm{0}}{\rm{.300}}\;{\rm{M}}$.

So, the correct answer is “Option C”.

Note:
For the determination of molarity two quantities are necessary they are volume and number of moles of the given substituents. The molarity has ${\rm{mol/L}}$.