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Chapter 14: Problem 56

A solution is prepared by adding \(50.0 \mathrm{~mL}\) of \(0.050 M \mathrm{HBr}\) to \(150.0 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) HI. Calculate \(\left[\mathrm{H}^{+}\right]\) and the \(\mathrm{pH}\) of this solution. \(\mathrm{HBr}\) and \(\mathrm{HI}\) are both considered strong acids.

Short Answer

Expert verified
In the given solution of a mixture of HBr and HI, the H+ ion concentration is approximately 0.0875 M, and the pH is approximately 1.06.

Step by step solution

01

Calculate the moles of HBr and HI in the solution

First, we will calculate the moles of HBr and HI in their respective solutions using the given concentrations and volumes. For HBr: Moles of HBr = (Concentration of HBr) × (Volume of HBr) Moles of HBr = 0.050 M × 50.0 mL Note: 1 L = 1000 mL, so we should convert mL to L in the case. Moles of HBr = 0.050 mol/L × (50.0 mL / 1000) Moles of HBr = 0.00250 mol For HI: Moles of HI = (Concentration of HI) × (Volume of HI) Moles of HI = 0.10 M × 150.0 mL Moles of HI = 0.10 mol/L × (150.0 mL / 1000) Moles of HI = 0.0150 mol
02

Calculate the total moles of H+ ions in the mixture

Since both HBr and HI release 1 mole of H+ ion per mole of the acid, the total moles of H+ ions in the mixture will be the sum of moles of HBr and HI. Total moles of H+ ions = Moles of HBr + Moles of HI Total moles of H+ ions = 0.00250 mol + 0.0150 mol Total moles of H+ ions = 0.0175 mol
03

Calculate the total volume of the solution

To determine the total volume of the solution, we will add the volumes of the HBr and HI solutions. Total volume of the solution = Volume of HBr + Volume of HI Total volume of the solution = 50.0 mL + 150.0 mL Total volume of the solution = 200.0 mL Don't forget to convert mL to L: Total volume of the solution = 200.0 mL / 1000 = 0.200 L
04

Calculate the H+ ion concentration in the mixture

Now, with the total moles of H+ ions and the total volume of the solution, we can calculate the H+ ion concentration in the mixture. [H+] = (Total moles of H+ ions) / (Total volume of the solution) [H+] = (0.0175 mol) / (0.200 L) [H+] = 0.0875 M
05

Calculate the pH of the solution

Finally, we can calculate the pH of the solution using the formula: \[ pH = -\log_{10}([H^{+}]) \] pH = -log10(0.0875) pH ≈ 1.06 So, the H+ ion concentration in the given solution is approximately 0.0875 M and the pH is approximately 1.06.

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Most popular questions from this chapter

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