Question

What volume of each of the following bases will react completely with \(25.00 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{HCl}\) ? a. \(0.100 \mathrm{M} \mathrm{NaOH}\) b. \(0.0500 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\) c. \(0.250 \mathrm{M} \mathrm{KOH}\)

Short answer

The volumes required to completely react with \(25.00 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{HCl}\) are: a) \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) b) \(50.0 \mathrm{~mL}\) of \(0.0500 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}\) c) \(20.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{KOH}\)

Step-by-step solution

Write balanced chemical equations

For each base, write the balanced chemical equation with HCl. a) NaOH + HCl -> NaCl + H2O b) Sr(OH)2 + 2HCl -> SrCl2 + 2H2O c) KOH + HCl -> KCl + H2O

Calculate moles of HCl

The initial volume of the given HCl solution is 25.00 mL, and its concentration is 0.200 M. The number of moles of HCl can be calculated as follows: moles of HCl = volume (L) × concentration (mol/L) moles of HCl = \(0.02500 L × 0.200 mol L^{-1} = 0.00500 mol\)

Calculate moles of each base

Using the mole ratios from the balanced chemical equations from Step 1, calculate the moles of each base needed for the reaction. a) NaOH: 1 mol NaOH reacts with 1 mol HCl, so moles of NaOH = moles of HCl = 0.00500 mol b) Sr(OH)2: 1 mol Sr(OH)2 reacts with 2 mol HCl, so moles of Sr(OH)2 = (0.00500 mol HCl) / 2 = 0.00250 mol c) KOH: 1 mol KOH reacts with 1 mol HCl, so moles of KOH = moles of HCl = 0.00500 mol

Calculate volume of each base

Finally, use the given concentration for each base to find the required volume that will completely react with the given HCl solution. a) Volume of NaOH: \(v = \dfrac{0.00500 mol}{0.100 mol L^{-1}} = 0.0500 L = 50.0 mL\) b) Volume of Sr(OH)2: \(v = \dfrac{0.00250 mol}{0.0500 mol L^{-1}} = 0.0500 L = 50.0 mL\) c) Volume of KOH: \(v = \dfrac{0.00500 mol}{0.250 mol L^{-1}} = 0.0200 L = 20.0 mL\) To summarize, the volumes required to completely react with 25.00 mL of 0.200 M HCl are: a) 50.0 mL of 0.100 M NaOH b) 50.0 mL of 0.0500 M Sr(OH)2 c) 20.0 mL of 0.250 M KOH

Key concepts

Chemical Equations

Writing a balanced chemical equation is the first step in understanding a titration reaction. It shows the interaction between an acid and a base, indicating which substances react and which products are formed. In our case:

• For NaOH and HCl: NaOH + HCl -> NaCl + H2O
• For Sr(OH)₂ and HCl: Sr(OH)₂ + 2HCl -> SrCl₂ + 2H₂O
• For KOH and HCl: KOH + HCl -> KCl + H2O

Each base has a different reaction equation based on its composition. For NaOH and KOH, which have one hydroxide ion (OH⁻), one mole of base reacts with one mole of HCl. In contrast, Sr(OH)₂ has two hydroxide ions, meaning one mole of Sr(OH)₂ reacts with two moles of HCl. Understanding these ratios is crucial for proceeding with calculations.

Mole Calculations

Mole calculations bridge the gap between the measurable volume and concentration of chemicals and their interactions at the molecular level. The number of moles of a substance in a solution can be calculated through the formula:
\[\text{moles} = \text{Volume} \,(L) \times \text{Concentration}\,(mol/L)\]For instance, with 25 mL of 0.200 M HCl, you calculate the moles of HCl as:
\[0.025 L \times 0.200 \ mol/L = 0.00500 \ mol\]Converting mL to liters (25 mL = 0.025 L) is essential for consistency in units.
Once you know the moles of HCl, these values are compared to the stoichiometric ratios in the balanced equations to find the moles of each base needed for the reaction.

Solution Concentration

Solution concentration indicates how much a solute is dissolved in a given amount of solvent, typically expressed in moles per liter (Molarity - M). In the context of titrations, knowing the concentration of the reactants is crucial for determining how much of each is needed to reach the equivalent point.

• For NaOH: 0.100 M
• For Sr(OH)₂: 0.0500 M
• For KOH: 0.250 M

These concentrations inform us about the amount of base in a given volume of solution. By comparing moles required from the balanced equations to the given concentrations, we can calculate the necessary volume of each base to completely react with the known amount of HCl.

Volume Calculation

Finally, volume calculation involves figuring out how much of a solution is required to achieve a complete reaction, using the formula:
\[\text{Volume} \,(L) = \dfrac{\text{moles of solute}}{\text{Concentration}\,(mol/L)}\]Let's apply this:

• For NaOH, with 0.00500 mol needed and a concentration of 0.100 mol/L: \[\dfrac{0.00500 \ mol}{0.100 \ mol/L} = 0.0500 \ L = 50.0 \ mL\]
• For Sr(OH)₂, with 0.00250 mol and a concentration of 0.0500 mol/L: \[\dfrac{0.00250 \ mol}{0.0500 \ mol/L} = 0.0500 \ L = 50.0 \ mL\]
• For KOH, with 0.00500 mol and 0.250 mol/L concentration: \[\dfrac{0.00500 \ mol}{0.250 \ mol/L} = 0.0200 \ L = 20.0 \ mL\]

This step shows the application of both concentration and stoichiometry to solve for how much of each reactant is needed.