The pH of saturated is found to be 13.12. A 15.0mL sample of saturated Sr(OH)2 is diluted to 250.0mL in a volumetric flask. A 15.0 mL sample of the diluted Sr(OH)2 is transferred to a beaker, and some water is added. The resulting solution requires 27.6mL of a HCl solution for its titration.What is the molarity of this HCl solution?
Sr(OH)2 ==> Sr^+2 + 2OH^-
pH = 13.12
pH + pOH = pKw = 14 and
pOH = 0.88; therefore, (OH^-) = 0.132
What is the concn of the OH- in the satd soln? It is 0.132. That 15 mL is diluted to 250; now the concn is 0.132 x 15/250 = 0.00792M. We take 15 mL of that and titrate it with HCl.
mLOH- x MOH- = mLHCl x MHCl
To find the molarity of the HCl solution, we can use the method of titration. In titration, we mix a known volume and concentration of one solution with an unknown volume and concentration of another solution until a reaction between the two is complete. By measuring the amount of the known solution required to react completely with the unknown solution, we can determine the concentration of the unknown solution.
In this case, the known solution is the HCl solution, and the unknown solution is the diluted Sr(OH)2 solution. The balanced chemical equation for the reaction between HCl and Sr(OH)2 is as follows:
2HCl + Sr(OH)2 -> SrCl2 + 2H2O
From the balanced equation, we can see that the ratio of HCl to Sr(OH)2 is 2:1. Therefore, the number of moles of HCl used in the titration is equal to twice the number of moles of Sr(OH)2.
First, let's calculate the number of moles of Sr(OH)2 in the 15.0 mL of the diluted solution that was transferred to the beaker. To do this, we will use the dilution equation:
C1V1 = C2V2
Where:
C1 = initial concentration of the Sr(OH)2 solution
V1 = initial volume of the Sr(OH)2 solution
C2 = final concentration of the Sr(OH)2 solution (which is what we are trying to find)
V2 = final volume of the Sr(OH)2 solution (which is given as 250.0 mL)
Since the initial volume (V1) is 15.0 mL and the initial concentration (C1) is unknown, we can rewrite the dilution equation as:
C1(15.0 mL) = C2(250.0 mL)
Now, we know from the given information that the pH of the saturated Sr(OH)2 solution is 13.12. Since pH is a measure of the concentration of hydrogen ions in a solution, we can use this information to find the concentration of hydroxide ions (OH-) in the saturated Sr(OH)2 solution.
pOH = 14 - pH
pOH = 14 - 13.12
pOH = 0.88
Now, we can find the concentration of hydroxide ions using the pOH:
[OH-] = 10^(-pOH)
[OH-] = 10^(-0.88)
[OH-] = 0.127 M
Since the balanced equation shows a 1:2 stoichiometric ratio between hydroxide ions and Sr(OH)2, the concentration of Sr(OH)2 is matched at 0.127 M.
Now, let's calculate the number of moles of Sr(OH)2 in the 15.0 mL sample:
moles of Sr(OH)2 = concentration × volume
moles of Sr(OH)2 = (0.127 M) × (0.015 L)
moles of Sr(OH)2 = 0.001905 moles
According to the balanced equation, we know that twice the number of moles of Sr(OH)2 is equal to the number of moles of HCl used in the titration. Therefore, the number of moles of HCl is:
moles of HCl = 2 × moles of Sr(OH)2
moles of HCl = 2 × 0.001905 moles
moles of HCl = 0.00381 moles
Finally, we can calculate the molarity of the HCl solution using the moles of HCl and the volume of HCl used in the titration (27.6 mL = 0.0276 L):
molarity of HCl = moles of HCl / volume of HCl
molarity of HCl = 0.00381 moles / 0.0276 L
molarity of HCl = 0.138 M
Therefore, the molarity of the HCl solution is 0.138 M.