Problem 63 - Chemistry The Science in Context

Question

How many milliliters of \(0.250 M\) NaOH are required to neutralize the following solutions? a. \(60.0 \mathrm{mL}\) of \(0.0750 M \mathrm{HCl}\) b. \(35.0 \mathrm{mL}\) of \(0.226 M \mathrm{HNO}_{3}\) c. \(75.0 \mathrm{mL}\) of \(0.190 M \mathrm{H}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

Question: Calculate the volume (in mL) of 0.250 M NaOH required to neutralize the following acidic solutions: a) 60.0 mL of 0.0750 M HCl b) 35.0 mL of 0.226 M HNO3 c) 75.0 mL of 0.190 M H2SO4 Answer: a) 18.0 mL b) 31.6 mL c) 114 mL

Step 1: Calculate moles of HCl

To calculate the moles of HCl, multiply its volume (in liters) by its molarity. The volume in liters is \(60.0 \mathrm{mL} \times \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.0600 \mathrm{L}\). Moles of HCl = Volume × Molarity = \(0.0600 \mathrm{L} \times 0.0750 \mathrm{M} = 0.00450 \mathrm{mol}\)

Step 2: Calculate moles of NaOH required for neutralization

The balanced chemical equation for the neutralization reaction is: \(\mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_{2}\mathrm{O}\). From the balanced equation, we can see that 1 mole of HCl reacts with 1 mole of NaOH. So, 0.00450 moles of HCl will react with 0.00450 moles of NaOH.

Step 3: Calculate the volume of 0.250 M NaOH required

To calculate the volume of 0.250 M NaOH required, divide the moles of NaOH by the molarity of NaOH and convert it to milliliters: Volume = \(\frac{0.00450 \mathrm{mol}}{0.250 \mathrm{M}} = 0.018 \mathrm{L} \times \frac{1000 \mathrm{mL}}{1 \mathrm{L}} = 18.0 \mathrm{mL}\) b) \(35.0 \mathrm{mL}\) of \(0.226 M \mathrm{HNO}_{3}\)

Step 1: Calculate moles of HNO3

To calculate the moles of HNO3, multiply its volume (in liters) by its molarity. The volume in liters is \(35.0 \mathrm{mL} \times \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.0350 \mathrm{L}\). Moles of HNO3 = Volume × Molarity = \(0.0350 \mathrm{L} \times 0.226 \mathrm{M} = 0.00791 \mathrm{mol}\)

Step 2: Calculate moles of NaOH required for neutralization

The balanced chemical equation for the neutralization reaction is: \(\mathrm{HNO}_{3} + \mathrm{NaOH} \rightarrow \mathrm{NaNO}_{3} + \mathrm{H}_{2}\mathrm{O}\). From the balanced equation, we can see that 1 mole of HNO3 reacts with 1 mole of NaOH. So, 0.00791 moles of HNO3 will react with 0.00791 moles of NaOH.

Step 3: Calculate the volume of 0.250 M NaOH required

To calculate the volume of 0.250 M NaOH required, divide the moles of NaOH by the molarity of NaOH and convert it to milliliters: Volume = \(\frac{0.00791 \mathrm{mol}}{0.250 \mathrm{M}} = 0.0316 \mathrm{L} \times \frac{1000 \mathrm{mL}}{1 \mathrm{L}} = 31.6 \mathrm{mL}\) c) \(75.0 \mathrm{mL}\) of \(0.190 M \mathrm{H}_{2} \mathrm{SO}_{4}\)

Step 1: Calculate moles of H2SO4

To calculate the moles of H2SO4, multiply its volume (in liters) by its molarity. The volume in liters is \(75.0 \mathrm{mL} \times \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.0750 \mathrm{L}\). Moles of H2SO4 = Volume × Molarity = \(0.0750 \mathrm{L} \times 0.190 \mathrm{M} = 0.0143 \mathrm{mol}\)

Step 2: Calculate moles of NaOH required for neutralization

The balanced chemical equation for the neutralization reaction is: \(\mathrm{H}_{2}\mathrm{SO}_{4} + 2\mathrm{NaOH} \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4} + 2\mathrm{H}_{2}\mathrm{O}\). From the balanced equation, we can see that 1 mole of H2SO4 reacts with 2 moles of NaOH. So, 0.0143 moles of H2SO4 will react with \(0.0143 \mathrm{mol} \times 2 = 0.0286 \mathrm{mol}\) of NaOH.

Step 3: Calculate the volume of 0.250 M NaOH required

To calculate the volume of 0.250 M NaOH required, divide the moles of NaOH by the molarity of NaOH and convert it to milliliters: Volume = \(\frac{0.0286 \mathrm{mol}}{0.250 \mathrm{M}} = 0.114 \mathrm{L} \times \frac{1000 \mathrm{mL}}{1 \mathrm{L}} = 114 \mathrm{mL}\)

Key Concepts

Neutralization

Neutralization is an essential concept in acid-base chemistry, where an acid and a base react to form water and a salt. This process effectively eliminates the acidic and basic properties of the reactants. During neutralization, the number of moles of hydrogen ions from the acid equates to the number of moles of hydroxide ions from the base, forming water in the process.

For example, consider the neutralization of hydrochloric acid (HCl) with sodium hydroxide (NaOH), which produces water (H extsubscript{2}O) and sodium chloride (NaCl), a common salt. The reason this reaction is significant is that it illustrates the core principle of neutralization, which is the complete reaction and cancellation of the acidic and basic properties of the reacting substances.

Understanding neutralization is crucial in calculating how much of an acid is needed to react exactly with a particular base. This calculation is based on the mole ratio from the balanced chemical equation.

Molarity Calculation

Molarity is a measure of the concentration of a solute in a solution, expressed as moles of solute per liter of solution (mol/L). It's an essential concept in chemistry because it allows us to quantitate the amount of solute in a given solution. Calculating molarity can help predict the outcomes of various chemical reactions, particularly in titration.

To calculate molarity effectively, the formula is simple: \[\text{Molarity} (M) = \frac{\text{moles of solute}}{\text{liters of solution}}\]This formula was used in the solution of the exercise. By converting the volume from milliliters to liters and using the given molarity, we calculated the moles of acid present in each solution before neutralization.

• For example, to find the moles of HCl, we multiply the volume (in liters) by its molarity.
• The solution's molarity provides a direct means to tie the volume of liquid reactant to the chemical moles needed for neutralization.

This understanding bridges the connection between physical quantities and chemical reactions, making conversions and calculations straightforward.

Balanced Chemical Equation

A balanced chemical equation provides the exact proportions in which reactants combine and products form. It is vital for understanding chemical reactions, ensuring that the law of conservation of mass is respected.

In an acid-base titration, it's crucial to use balanced equations to determine the stoichiometric relationships between the reactants. For each of the given problems in the exercise, the balanced chemical equation highlights the mole ratio, which is fundamental for calculations.

Consider the balance equation of \[\mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_{2} ext{O}\]Here, we see a 1:1 molar ratio of HCl to NaOH. This means for each mole of HCl, one mole of NaOH is required for complete neutralization.

• However, for sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)), the equation is different:
• \[\mathrm{H}_{2}\mathrm{SO}_{4} + 2\mathrm{NaOH} \rightarrow \mathrm{Na}_2\mathrm{SO}_{4} + 2\mathrm{H}_{2}\mathrm{O}\]implies a 1:2 mole ratio.

By understanding these equations, it becomes much simpler to identify the necessary amount of base required to fully neutralize a given acid and vice versa.