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Chapter 4: Problem 90

Calculate the concentration (in molarity) of a \(\mathrm{NaOH}\) solution if \(25.0 \mathrm{~mL}\) of the solution are needed to neutralize \(17.4 \mathrm{~mL}\) of a \(0.312 \mathrm{M} \mathrm{HCl}\) solution.

Short Answer

Expert verified
The molarity of the NaOH solution is \(0.217152 M\)

Step by step solution

01

Convert volumes from mL to L

First convert the given volumes from milliliters to liters because molarity is usually expressed in terms of liters. This can be done by dividing the given volume by 1000, as 1L equals 1000mL. So, \(25.0 \mathrm{~mL}\) becomes \(0.025 \mathrm{~L}\) and \(17.4\mathrm{~mL}\) becomes \(0.0174\mathrm{~L}\)
02

Understand the chemical reaction

In this neutralization reaction, Sodium Hydroxide (NaOH) reacts with Hydrochloric Acid (HCl) to produce water and Sodium Chloride (NaCl), given by the balanced equation: \(NaOH + HCl 鈫� H2O + NaCl\). This reaction is a 1:1 reaction, so the number of moles for HCl equals that of NaOH.
03

Calculate the number of moles of HCl

The number of moles of HCl can be calculated using the given molarity and volume of HCl. The molarity of a solution equals the number of moles divided by the volume. So, number of moles equals molarity multiplied by volume, which gives \(0.312 M \times 0.0174 L = 0.0054288 moles\) of HCl.
04

Find the molarity of NaOH

Because the reaction is 1:1, the number of moles of HCl equals the number of moles of NaOH. So, there are \(0.0054288 \mathrm{moles}\) of NaOH. The molarity of NaOH can then be calculated by dividing the number of moles by the volume, which gives \( \frac{0.0054288 moles}{0.025 L} = 0.217152 M\)

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Key Concepts

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

Neutralization Reaction
A neutralization reaction involves an acid and a base reacting with each other to produce water and a salt. It is an important type of chemical reaction. In our exercise, Hydrochloric Acid (HCl) is the acid and Sodium Hydroxide (NaOH) is the base.

When they react, the hydrogen ions ( H^+) from the acid combine with the hydroxide ions ( OH^- ) from the base to form water ( H_2O ). This is what makes the solution neutral, as water has a neutral pH.
  • Neutralization reactions are crucial in everyday life, like in antacid tablets that neutralize stomach acid.
  • This type of reaction can be represented using simple balanced chemical equations.
Understanding the concept of neutralization helps in predicting the products formed in the reaction and calculating concentrations, such as molarity, needed to fully react the components.
Chemical Reaction
A chemical reaction involves rearranging the molecular or ionic structure of substances involved, forming new products.

In the context of our exercise, the chemical reaction occurs between HCl and NaOH, resulting in water and NaCl.
This transformation involves breaking and forming of bonds, thus converting reactants to products.
  • This particular reaction is a 1:1 molar ratio, so one mole of HCl reacts with one mole of NaOH.
  • Recognition of the type of chemical reaction helps in planning how to achieve complete reaction, hence how much of each reactant is needed.
Chemical reactions are fundamental in the study of chemistry, providing knowledge on how various substances interact and transform.
Moles
The mole is a standard unit of measurement used in chemistry to express amounts of a chemical substance.

One mole is equivalent to Avogadro's number (6.022 imes 10^{23}) of particles, be they atoms, molecules, ions, etc.
In the step where we found the number of moles of HCl, we used the formula \(\text{moles} = \text{molarity} \times \text{volume}\).

The number of moles gives us the amount of substance in a reaction, important for calculating how much is needed or produced.
  • In our exercise, knowing moles allows us to determine that 0.0054288 moles of NaOH are required to react completely with HCl.
  • Mastering the concept of moles is essential to navigate through any chemical reaction analysis effectively.
Balanced Chemical Equation
A balanced chemical equation is one where the number of atoms for each element is the same on both sides of the equation.

In our example, \(\text{NaOH} + \text{HCl} \rightarrow \text{H}_2\text{O} + \text{NaCl}\), each side of the equation has one sodium, one chlorine, two hydrogen, and one oxygen atom.
This balance ensures that the mass and charge are the same before and after the reaction.

Balanced equations are crucial because they allow for the calculation of unknown quantities of reactants or products, and confirm that matter is conserved.
  • These equations are resolved using coefficients, ensuring that the same number of atoms are on both sides.
  • In our computation, the balanced equation allows us to use the 1:1 ratio of HCl to NaOH to find their respective moles.
Understanding how to balance equations is foundational for all subsequent work in chemistry.

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Most popular questions from this chapter

A 325-mL sample of solution contains \(25.3 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\). (a) Calculate the molar concentration of \(\mathrm{Cl}^{-}\) in this solution. (b) How many grams of \(\mathrm{Cl}^{-}\) are in \(0.100 \mathrm{~L}\) of this solution?

Describe the basic steps involved in an acid-base titration. Why is this technique of great practical value?

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) is one of the most important nitrogen-containing fertilizers. Its purity can be analyzed by titrating a solution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) with a standard \(\mathrm{NaOH}\) solution. In one experiment a \(0.2041-\mathrm{g}\) sample of industrially prepared \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) required \(24.42 \mathrm{~mL}\) of \(0.1023 \mathrm{M} \mathrm{NaOH}\) for neutralization. (a) Write a net ionic equation for the reaction. (b) What is the percent purity of the sample?

What volume of \(0.416 M \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) should be added to \(255 \mathrm{~mL}\) of \(0.102 \mathrm{M} \mathrm{KNO}_{3}\) to produce a solution with a concentration of \(0.278 M \mathrm{NO}_{3}^{-}\) ions? Assume volumes are additive.

Give a chemical explanation for each of the following: (a) When calcium metal is added to a sulfuric acid solution, hydrogen gas is generated. After a few minutes, the reaction slows down and eventually stops even though none of the reactants is used up. (b) In the activity series, aluminum is above hydrogen, yet the metal appears to be unreactive toward steam and hydrochloric acid. (c) Sodium and potassium lie above copper in the activity series. In your explanation, discuss why \(\mathrm{Cu}^{2+}\) ions in a \(\mathrm{CuSO}_{4}\) solution are not converted to metallic copper upon the addition of these metals. (d) A metal M reacts slowly with steam. There is no visible change when it is placed in a pale green iron(II) sulfate solution. Where should we place \(\mathrm{M}\) in the activity series? (e) Before aluminum metal was obtained by electrolysis, it was produced by reducing its chloride \(\left(\mathrm{AlCl}_{3}\right)\) with an active metal. What metals would you use to produce aluminum in that way?
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