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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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

pH calculation
Understanding pH calculation is crucial when working with acids and bases. The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm of the hydrogen ion concentration: - pH = -log extsubscript{10}[H extsuperscript{+}] For a neutral solution at room temperature, a pH of 7 is characteristic. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution. When calculating pH, remember the relationship with hydrogen ion concentration - For pH 0, [H extsuperscript{+}] = 10 extsuperscript{0} = 1 M This means the solution is highly acidic. Calculating the pH involves transforming the concentration into a logarithmic scale, making it more manageable to compare acidity levels across different solutions.
molarity and volume relationship
In chemistry, molarity represents the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution (mol/L). To find the number of moles present in a given volume of a solution, use the formula: - Moles = Molarity (M) × Volume (L) This relationship is handy for determining how much of a reactant is present at any point in a reaction. For instance, in the original exercise, a solution of NaOH with a molarity of 2.0 M in a volume of 1.0 L contains: - 2.0 M × 1.0 L = 2.0 moles of NaOH Understanding this relationship helps to correctly calculate the reactants and products involved in a chemical reaction, ensuring the right amount of each compound is present or needed.
stoichiometry
Stoichiometry embodies the principles of chemistry that describe the quantitative relationships of reactants and products in a chemical reaction. It involves using balanced chemical equations to understand molecular conversion. In the context of the exercise, stoichiometry guided us in finding the amount of HCl needed to neutralize NaOH: - NaOH + HCl → NaCl + H extsubscript{2}O The stoichiometry from this reaction indicates a 1:1 molar relationship between NaOH and HCl. This ratio means that each mole of NaOH requires exactly one mole of HCl to completely convert into NaCl and water. Understanding stoichiometry is essential for accurately predicting the outcomes of reaction conditions and scaling reactions.
HCl neutralization
Hydrochloric Acid (HCl) is a common strong acid used in neutralization reactions with bases like NaOH. In these reactions, acids and bases react to form water and a salt. The key equation in neutralization: - Acid + Base → Salt + Water In the exercise above, HCl neutralizes NaOH: - NaOH + HCl → NaCl + H extsubscript{2}O Since both hydrochloric acid and sodium hydroxide dissociate completely in water, they react in a straightforward manner. Each mole of HCl neutralizes one mole of NaOH, resulting in the formation of sodium chloride (common table salt) and water. This process lowers the pH to a neutral level. Neutralization reactions are foundational in acid-base chemistry, helping to maintain pH balance in various chemical and biological systems.
chemical equations
Chemical equations are symbolic representations of chemical reactions, where reactants are transformed into products. A balanced chemical equation accurately represents the conservation of mass, meaning the quantity of each element remains constant throughout a chemical reaction. For example, the neutralization reaction in the exercise is represented by the chemical equation: - NaOH + HCl → NaCl + H extsubscript{2}O The balanced equation indicates: - Each reactant and product has equal numbers of atoms on both sides of the reaction Balancing chemical equations involves adjusting coefficients in front of reactants/products so the number of atoms for each element is equal on both sides of the equation. It ensures the mass is conserved, and it depicts how molecules interact during the reaction. Understanding how to read and balance chemical equations is vital for studying reactions and predicting the resulting products from various reactants.

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Most popular questions from this chapter

Amino acids are the building blocks for all proteins in our bodies. A structure for the amino acid alanine is All amino acids have at least two functional groups with acidic or basic properties. In alanine, the carboxylic acid group has \(K_{\mathrm{a}}=4.5 \times 10^{-3}\) and the amino group has \(K_{\mathrm{b}}=\) \(7.4 \times 10^{-5} .\) Because of the two groups with acidic or basic properties, three different charged ions of alanine are possible when alanine is dissolved in water. Which of these ions would predominate in a solution with \(\left[\mathrm{H}^{+}\right]=1.0\) \(\mathrm{M} ?\) In a solution with \(\left[\mathrm{OH}^{-}\right]=1.0\) \(\mathrm {M} ?\)

Could a buffered solution be made by mixing aqueous solutions of HCl and NaOH? Explain. Why isn't a mixture of a strong acid and its conjugate base considered a buffered solution?

You have a solution of the weak acid HA and add some HCl to it. What are the major species in the solution? What do you need to know to calculate the \(\mathrm{pH}\) of the solution, and how would you use this information? How does the \(\mathrm{pH}\) of the solution of just the HA compare with that of the final mixture? Explain.

Carbonate buffers are important in regulating the pH of blood at \(7.40 .\) If the carbonic acid concentration in a sample of blood is 0.0012 \(M,\) determine the bicarbonate ion concentration required to buffer the \(\mathrm{pH}\) of blood at \(\mathrm{pH}=7.40\). \(\mathrm{H}_{2} \mathrm{CQ}_{3}(a g) \rightleftharpoons \mathrm{HCQ}_{3}^{-}(a g)+\mathrm{H}^{+}(a g) \quad \) \(K_{\mathrm{a}}=4.3 \times 10^{-7}\)

Two drops of indicator HIn \(\left(K_{\mathrm{a}}=1.0 \times 10^{-9}\right),\) where HIn is yellow and \(\operatorname{In}^{-}\) is blue, are placed in \(100.0 \mathrm{mL}\) of \(0.10 \mathrm{M}\) HCl. a. What color is the solution initially? b. The solution is titrated with 0.10 \(M\) NaOH. At what pH will the color change (yellow to greenish yellow) occur? c. What color will the solution be after \(200.0 \mathrm{mL}\) NaOH has been added?

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