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Chapter 14: Problem 88

What quantity (moles) of HCl(g) must be added to \(1.0 \mathrm{L}\) of \(2.0 \mathrm{M}\) NaOH to achieve a pH of 0.00? (Neglect any volume changes.)

Short Answer

Expert verified
To achieve a pH of 0.00 in a 1.0 L of 2.0 M NaOH solution, 3.0 moles of HCl(g) must be added.

Step by step solution

01

Calculate the initial moles of NaOH in the solution

To begin, we need to determine the initial moles of NaOH in the solution. We can use the molarity formula: Moles = Molarity × Volume Given that the initial concentration of NaOH is 2.0 M and the volume is 1.0 L, we can calculate the moles of NaOH: Moles of NaOH = 2.0 M × 1.0 L Moles of NaOH = 2.0 moles
02

Determine moles of HCl needed to neutralize NaOH

To fully neutralize the NaOH, we can use the stoichiometric ratio from the balanced equation: NaOH + HCl → NaCl + H₂O Since the ratio between NaOH and HCl is 1:1, the moles of HCl needed to neutralize the NaOH are equal to the moles of NaOH: Moles of HCl (to neutralize) = Moles of NaOH Moles of HCl (to neutralize) = 2.0 moles
03

Calculate the moles of HCl required to achieve a pH of 0.00

To find the additional moles of HCl needed to reach a pH of 0.00, we must first determine the concentration of H+ ions needed in the final solution. The pH is given by: pH = -log_10[H+] Since we desire a pH of 0.00, we start with: 0.00 = -log_10[H+] Now, solving for [H+]: [H+] = 10^0 = 1 M With the desired [H+] concentration, we can now calculate the moles of HCl required. Notice that since we are neglecting any volume changes, the final volume is still 1.0 L. Moles of HCl (to achieve pH 0) = (1 M H+) × (Volume) Moles of HCl (to achieve pH 0) = 1 M × 1.0 L = 1.0 mole
04

Calculate the total moles of HCl needed

To find the total moles of HCl required, we need to sum up the moles of HCl needed to neutralize the NaOH and the moles of HCl needed to reach the pH of 0.00: Total moles of HCl = Moles of HCl (to neutralize) + Moles of HCl (to achieve pH 0) Total moles of HCl = 2.0 moles + 1.0 mole Total moles of HCl = 3.0 moles Thus, to achieve a pH of 0.00, 3.0 moles of HCl(g) must be added to the 1.0 L of 2.0 M NaOH solution.

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Most popular questions from this chapter

Consider the titration of \(100.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{NNH}_{2}\) \(\left(K_{\mathrm{b}}=3.0 \times 10^{-6}\right)\) by \(0.200 M\) HNO \(_{3}\). Calculate the pH of the resulting solution after the following volumes of \(\mathrm{HNO}_{3}\) have been added. a. \(0.0 \mathrm{mL}\) b. \(20.0 \mathrm{mL}\) c. \(25.0 \mathrm{mL}\) d. \(40.0 \mathrm{mL}\) e. \(50.0 \mathrm{mL}\) f. \(100.0 \mathrm{mL}\)

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