Calculate the concentration of an aqueous \(\mathrm{Sr}(\mathrm{OH})_{2}\) that has \(\mathrm{pH}=10.50\) .

Short Answer

Expert verified
The concentration of the aqueous Sr(OH)₂ solution with a pH of 10.50 is approximately \(1.58 \times 10^{-4}\) M.

Step by step solution

01

Convert pH to pOH

First, we need to convert the given pH value into pOH. This is necessary because we are dealing with a base (Sr(OH)₂) and need to find the concentration of hydroxide ions (OH⁻). The relationship between pH and pOH is: pH + pOH = 14 Given that pH = 10.50, we can find the value of pOH: pOH = 14 - pH pOH = 14 - 10.50 pOH = 3.50
02

Determine the concentration of hydroxide ions

Now that we have the pOH value, we can use the relationship between pOH and the concentration of hydroxide ions in the solution to find the concentration of OH⁻ ions: pOH = -log₁₀[OH⁻] Let [OH⁻] represent the concentration of hydroxide ions. We can rearrange the formula above to find [OH⁻]: [OH⁻] = 10^(-pOH) Substitute the value of pOH we found in Step 1: [OH⁻] = 10^(-3.50) [OH⁻] ≈ 3.16 × 10^(-4) M
03

Find the concentration of Strontium Hydroxide

Now that we have the concentration of hydroxide ions, we can use the formula of Sr(OH)₂ to find its concentration in the aqueous solution. Each molecule of Sr(OH)₂ dissociates into one Sr²⁺ ion and two OH⁻ ions: Sr(OH)₂ → Sr²⁺ + 2 OH⁻ The stoichiometric relationship between Sr(OH)₂ and OH⁻ is 1:2, which means: [Sr(OH)₂] = ([OH⁻])/2 Substitute the concentration of OH⁻ we found in Step 2: [Sr(OH)₂] = (3.16 × 10^(-4) M)/2 [Sr(OH)₂] ≈ 1.58 × 10^(-4) M The concentration of the aqueous Sr(OH)₂ solution is approximately 1.58 × 10^(-4) M.

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