Question

A \[100ml\] each of \[1M\]\[AgN{O_3}\] and \[1M\]\[NaCl\] are mixed. The nitrate ion concentration in the resulting solution is?
A.\[1M\]
B.\[0.5M\]
C.\[0.75M\]
D.\[0.25M\]

Answer 1

:Hint:Here in the question we have two compounds with the same volume and molarity. When both the compounds are mixed nitrate ions will have different concentrations. We will use the formula for molarity or concentration of mixed compounds.
Formula Used:
Molarity of mixture
\[M' = \dfrac{{{M_1}{V_1}}}{{{V_1} + {V_2}}}\]
Where \[M'\] is the resulting concentration,
\[{M_1}\] is the Molarity of substance,
\[{V_1},{V_2}\] are the volumes of solution

Complete step by step answer:
First, we will write the given quantities from the question.
\[{M_1} = {M_2} = 1M,{V_1} = {V_2} = 100ml\]
Here \[{M_1}\] is the molarity of \[AgN{O_3}\],
\[{M_2}\] is the molarity of \[NaCl\],
Now to find the concentration of nitrate ion, we will use the given quantities and substitute them in the formula of resulting concentration of the ion.
The formula is given as \[M' = \dfrac{{{M_1}{V_1}}}{{{V_1} + {V_2}}}\]. Now we will substitute the values in the given formula,
\[M' = \dfrac{{{M_1}{V_1}}}{{{V_1} + {V_2}}} = \dfrac{{1 \times 100}}{{100 + 100}}\]
\[ \Rightarrow M' = 0.5M\].
Hence, the concentration of nitrate ion in the resulting solution is \[0.5M\] .

Therefore, the correct option is (B).

Note:
The molarity of a solution is defined as the ratio of the number of moles of solute to the volume of the solution. Molarity is expressed in mole per liter.
It is represented by capital \[M\].
There are various ways to represent concentration terms for example in percentage, parts per million, and parts per billion.
Parts per million is represented by ppm. It is expressed as the ratio of the mass of solute to the mass of solution multiplied by \[{10^6}\].
Parts per billion is represented by ppb. It is expressed as a ratio of the mass of solute to the mass of solution multiplied by \[{10^9}\]
The volume of the solution and the molarity will not be the same every time.
Molarity and molality both are concentration terms but molarity is a temperature-dependent term.