Question

What volume of each of the following acids will react completely with \(50.00 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{NaOH} ?\) a. \(0.100 \mathrm{M} \mathrm{HCl}\) b. \(0.150 \mathrm{MHNO}_{3}\) c. \(0.200 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) ( 1 acidic hydrogen)

Short answer

The volume of each acid required for a complete reaction with \(50.00 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{NaOH}\) is: a. \(100.00 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) b. \(66.67 \mathrm{mL}\) of \(0.150 \mathrm{M} \mathrm{HNO}_{3}\) c. \(50.00 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

Step-by-step solution

Find the number of moles of NaOH

Given the volume and concentration of NaOH, we can calculate the moles of NaOH using the formula: Moles of NaOH = Volume (L) × Concentration (M) Since the volume is given in mL, we'll convert it to L by dividing by 1000: Volume in L = 50.00 mL / 1000 = 0.05000 L Now, we can find the moles of NaOH: Moles of NaOH = 0.05000 L × 0.200 M = 0.01000 mol

Determine the volume of acid needed for each reaction

We'll use stoichiometry to determine the volume of each acid required for a complete reaction with NaOH. The balanced chemical equation for the reaction between each acid and NaOH is: Acid + NaOH → Na+ (aq) + other products The mole ratio between each acid and NaOH is 1:1. Therefore, the moles of each acid required for complete reaction are equal to the moles of NaOH. a. For 0.100 M HCl: Volume of HCl = Moles of HCl / Concentration of HCl = 0.01000 mol / 0.100 M = 0.100 L or 100.00 mL b. For 0.150 M HNO3: Volume of HNO3 = Moles of HNO3 / Concentration of HNO3 = 0.01000 mol / 0.150 M = 0.06667 L or 66.67 mL c. For 0.200 M HC2H3O2 (1 acidic hydrogen): Volume of HC2H3O2 = Moles of HC2H3O2 / Concentration of HC2H3O2 = 0.01000 mol / 0.200 M = 0.05000 L or 50.00 mL So, the volume of each acid required for a complete reaction with 50.00 mL of 0.200 M NaOH is: a. 100.00 mL of 0.100 M HCl b. 66.67 mL of 0.150 M HNO3 c. 50.00 mL of 0.200 M HC2H3O2

Key concepts

Molarity

Molarity is an essential concept in chemistry that helps us understand the concentration of a solution. It's expressed as moles of solute divided by liters of solution. Molarity (M) reflects how many moles of a particular substance, like an acid or base, are present in a liter of solution.
When calculating molarity, you often use the formula:

• Molarity (M) = Moles of solute / Volume of solution in liters.

For example, if we consider NaOH from the exercise with a molarity of 0.200 M, it signifies that there are 0.200 moles of NaOH in every liter of the solution. This concentration helps determine how much acid is needed to neutralize a specific volume of NaOH. Understanding molarity is crucial for tasks like preparing solutions and carrying out precise chemical reactions.

Stoichiometry

In chemistry, stoichiometry involves calculating the quantities of reactants and products in chemical reactions. It is crucial for understanding how different substances react in fixed proportions based on balanced chemical equations.
For the exercise, stoichiometry helps determine how much acid is needed to neutralize the given amount of NaOH. The balanced chemical reactions are represented by the equation:

• Acid + NaOH → Na⁺ (aq) + products

Here, the stoichiometric coefficients let us know that the molar ratio between NaOH and each acid (HCl, HNO₃, and HC₂H₃O₂) is 1:1. This means 1 mole of each acid will react with 1 mole of NaOH. The application of stoichiometry allows us to calculate that the number of moles of acid needed will be exactly equal to the moles of NaOH.

Chemical Reactions

Chemical reactions entail the transformation of substances through the breaking and forming of chemical bonds. When acids and bases react, they undergo a neutralization reaction, forming water and a salt.
In the context of the exercise, each acid such as HCl, HNO₃, or HC₂H₃O₂ reacts with NaOH. Each reaction follows the general pattern:

• Acid + NaOH → Na⁺ (aq) + anions + H₂O

This reaction results in the production of a neutral compound (often water) and a salt (like NaCl for HCl and NaOH). Understanding these reactions helps predict the outcome of mixing certain chemicals, including energy changes and product formation.

Volume Calculations

Volume calculations in chemistry enable us to figure out how much liquid we need to combine with other chemicals in a solution or reaction. It's especially important when dealing with solutions of known concentrations, like those given in molarity units.
In the exercise, after determining the moles of NaOH, we needed to calculate how much of each acid would be necessary to neutralize it. Using the formula:

• Volume of solution (L) = Moles of solute / Molarity

we calculated that for the concentrated solutions of HCl, HNO₃, and HC₂H₃O₂, the volumes needed were 100.00 mL, 66.67 mL, and 50.00 mL respectively. These calculations are essential for precise laboratory work and ensure efficient use of reactants in reactions.