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Question: \( 50{\text{ mL}} \) of \( {H_2}O \) is added to \( 50{\text{ mL}} \) of \( 1 \times {10^{ - 3}}M \)...

50 mL50{\text{ mL}} of H2O{H_2}O is added to 50 mL50{\text{ mL}} of 1×10−3M1 \times {10^{ - 3}}M barium hydroxide solution. What is the pH of the resulting solution?
A. 3.03.0
B. 3.33.3
C. 11.011.0
D. 11.711.7

Explanation

Solution

Dilution is used to decrease the concentration of solute. A solution having a high concentration of hydrogen ions has low pH whereas the solutions having a low concentration of hydrogen ions have high pH. The concentrations and volumes after and before dilution can be related to the equation M1V1=M2V2{M_1}{V_1} = {M_2}{V_2} .

Complete answer:
The chemical formula of Barium hydroxide is Ba(OH)2Ba{(OH)_2}
The volume and molarity before and after dilution can be given by M1V1=M2V2{M_1}{V_1} = {M_2}{V_2} …(I)
Given, initial volume V1=50{V_1} = 50 Ml
Initial molarity M1=1×10−3M{M_1} = 1 \times {10^{ - 3}}M
The volume of the resulting solution V2=100 mL{V_2} = 100{\text{ }}mL
Substituting the given values in equation (I)
1×10−3×50 mL=100 mL×M21 \times {10^{ - 3}} \times 50{\text{ mL}} = 100{\text{ mL}} \times {M_2}
M2=1×10−3×50100{M_2} = \dfrac{{1 \times {{10}^{ - 3}} \times 50}}{{100}}
M2=0.5×10−3M{M_2} = 0.5 \times {10^{ - 3}}M
One mole of barium hydroxide i.e. Ba(OH)2Ba{(OH)_2} can give 2 moles of OH−O{H^ - } ions.
Ba(OH)2→Ba2++2OH−Ba{(OH)_2} \to B{a^{2 + }} + 2O{H^ - }
So it can be concluded that the concentration of hydroxide ions is 2 times the concentration of barium hydroxide solution.
[OH]−=2×0.5×10−3⇒1×10−3{[OH]^ - } = 2 \times 0.5 \times {10^{ - 3}} \Rightarrow 1 \times {10^{ - 3}}
pOH is the measure of hydroxide ion concentration so,
p[OH]=−log⁡[OH]p[OH] = - \log [OH]
p[OH]=−log⁡[10−3]p[OH] = - \log [{10^{ - 3}}]
p[OH]=3p[OH] = 3
We know that the sum of pH and pOH is 14.
pH+pOH=14pH + pOH = 14
pH + 3 = 14
pH=11pH = 11
The pH of the resulting solution is 11.0
Therefore the correct answer is option C.

Note:
An equation of chemical reaction which has the number of atoms in the reaction for each element and for both the reactants and the products the total charge is equal then it is a balanced equation. In simple words the number of atoms is the same on both, reactants, as well as products side in a balanced reaction, coefficient (a whole number), is added to the element or compound in the equation.