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Question: The \( pH \) of milk of magnesia, a suspension of solid magnesium hydroxide in a saturated aqueous s...

The pHpH of milk of magnesia, a suspension of solid magnesium hydroxide in a saturated aqueous solution is 10.5210.52 . What is the molarity of OH−O{H^ - } ions in the saturated aqueous solution? The suspended undissolved Mg(OH)2Mg{(OH)_2} does not affect the measurement.
(A) 3×10−4M3 \times {10^{ - 4}}M
(B) 1.7×10−4M1.7 \times {10^{ - 4}}M
(C) 2.5×10−4M2.5 \times {10^{ - 4}}M
(D) 3.6×10−4M3.6 \times {10^{ - 4}}M

Explanation

Solution

if the pHpH of the solution is given, pOHpOH can be easily calculated using the formula:
pH+pOH=14pH + pOH = 14
After getting the value of pOHpOH , OH−O{H^ - } ion can be calculated using the formula:
pOH=−log⁡[OH−]pOH = - \log [O{H^ - }]

Complete step by step solution:
In this question, we are given the pHpH of solution (milk of magnesia). To calculate the concentration of OH−O{H^ - } ion, we need to find pOHpOH by using the formula:
pH+pOH=14pH + pOH = 14
Substituting the value of pHpH as given in the question,
⇒10.52+pOH=14\Rightarrow 10.52 + pOH = 14
⇒pOH=14−10.52\Rightarrow pOH = 14 - 10.52
⇒pOH=3.48\Rightarrow pOH = 3.48
Now, we have the value of pOHpOH . So, we can calculate the concentration of OH−O{H^ - } ion by using the formula:
pOH=−log⁡[OH−]pOH = - \log [O{H^ - }]
On rearranging the formula, we get;
⇒−pOH=log⁡[OH−]\Rightarrow - pOH = \log [O{H^ - }]
⇒[OH−]=10−pOH\Rightarrow [O{H^ - }] = {10^{ - pOH}}
Substituting the value of pOHpOH ,
⇒[OH−]=10−3.48\Rightarrow [O{H^ - }] = {10^{ - 3.48}}
⇒[OH−]=0.0003\Rightarrow [O{H^ - }] = 0.0003
⇒[OH−]=3×10−4M\Rightarrow [O{H^ - }] = 3 \times {10^{ - 4}}M
Hence, the molarity of OH−O{H^ - } ion in the saturated aqueous solution is 3×10−4M3 \times {10^{ - 4}}M .
So, the correct option is option (A).

Additional information:
Magnesium is a naturally occurring mineral. Milk of magnesia is used as a laxative to relieve occasional constipation. It is also used as an antacid to relieve indigestion, sour stomach, and heartburn. Milk of magnesia works by absorbing water and neutralizing acid.

Note:
In any question, if we are given pHpH or pOHpOH of solution then we can easily calculate the concentration of OH−O{H^ - } ions in the solution by using the appropriate formula mentioned above.
Calculation mistakes should be avoided while taking antilogarithms in some cases.