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Chapter 9: Problem 61

A 0.1036 -g sample that contains only \(\mathrm{BaCl}_{2}\) and \(\mathrm{NaCl}\) is dissolved in \(50 \mathrm{~mL}\) of distilled water. Titrating with \(0.07916 \mathrm{M} \mathrm{AgNO}_{3}\) requires \(19.46 \mathrm{~mL}\) to reach the Fajans end point. Report the \(\% \mathrm{w} / \mathrm{w} \mathrm{BaCl}_{2}\) in the sample.

Short Answer

Expert verified
The sample is approximately 29.96% w/w BaCl鈧�.

Step by step solution

01

Determine Moles of AgCl Produced

Using the titration data, we calculate the moles of silver nitrate (AgNO鈧�) used, which corresponds to the moles of chloride ions precipitated as silver chloride (AgCl). Given that the concentration of the silver nitrate solution is 0.07916 M and the volume used is 19.46 mL, we convert the volume to liters and use the formula: \[ \text{moles of AgCl} = 0.07916 \text{ M} \times \frac{19.46}{1000} \text{ L} = 0.001540 \text{ moles} \]
02

Calculate Moles of Cl鈦� in Mixture

Each mole of AgCl results from one mole of Cl鈦�. Therefore, the moles of Cl鈦� in the mixture is the same as the moles of AgCl produced: 0.001540 moles of Cl鈦�.
03

Set Up System of Equations

Let \( x \) be the moles of BaCl鈧� and \( y \) be the moles of NaCl. The equations are based on mass and chloride balance. The chloride balance equation is: \[ 2x + y = 0.001540 \] And the mass balance equation based on the molar masses of BaCl鈧� (208.23 g/mol) and NaCl (58.44 g/mol) gives: \[ 208.23x + 58.44y = 0.1036 \text{ g} \]
04

Solve the System of Equations

First, solve for \( y \) in terms of \( x \) using the chloride balance equation: \[ y = 0.001540 - 2x \] Then substitute \( y \) into the mass balance equation: \[ 208.23x + 58.44(0.001540 - 2x) = 0.1036 \] Simplifying gives: \[ 208.23x + 0.0899676 - 116.88x = 0.1036 \] \[ 91.35x = 0.0136324 \] \[ x = 0.0001492 \text{ moles of BaCl}_2 \]
05

Calculate Mass % of BaCl鈧�

Determine the mass of BaCl鈧� using its moles: \( 0.0001492 \times 208.23 = 0.031048 \text{ g} \). Find the mass percent of BaCl鈧� in the sample by: \[ \frac{0.031048}{0.1036} \times 100 \approx 29.96\% \]
06

Final Verification

Verify the calculations with both the mass of Cl鈦� and total mass balance to ensure consistency. The obtained values satisfy both equations, confirming the percentage calculated.

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Key Concepts

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

Chloride Ion Titration
In the field of analytical chemistry, chloride ion titration is a valuable technique used for quantifying the amount of chloride ions in a solution. This method involves the use of a titrant, typically silver nitrate (\(\text{AgNO}_3\)), which reacts specifically with chloride ions (\(\text{Cl}^-\)) to form a precipitate, silver chloride (\(\text{AgCl}\)). The point at which all chloride ions have reacted and precipitated is referred to as the endpoint of the titration, often indicated visually by a change in color due to an added indicator or via conductivity methods.
  • The equivalence point is when concentrations of reactants match stoichiometrically.
  • Light-sensitive silver chloride forms, allowing precise measurement of chloride ions.
  • Commonly used for analyzing salt solutions and mixtures containing chloride ions.
Chloride ion titration is crucial in projects where precise ion concentration is required, such as water quality testing and various industrial applications.
Fajans Method
The Fajans method is a specific type of titration used in analytical chemistry to accurately determine the end point of a precipitation reaction. Named after the chemist Kazimierz Fajans, this method enhances the precision of titration by utilizing adsorption indicators which change color upon binding to the precipitate's surface, signaling the end of the titration.
  • Upon reaching the end point, any further addition of \(\text{Ag}^+\) ions causes a visible color change.
  • These dyes are chosen for their ability to adsorb at the precipitate surface before more precipitate forms.
  • The color shift offers a stark visual cue, optimizing accuracy in determining when titration is complete.
The method is especially advantageous when working with compounds like silver halides, where the precipitate's nature might obscure traditional visual cues.
Mass Percent Calculation
Mass percent calculation in chemistry is a straightforward technique to find the percentage composition of a component within a mixture or compound. In essence, it allows us to compare the mass of one part with the total mass of the sample. To derive it, one must first determine the mass of the specific component and then divide this value by the total mass of the mixture, multiplying by 100 to convert to a percentage.
  • Formula: \[\text{Mass percent} = \left(\frac{\text{mass of component}}{\text{total mass of sample}}\right) \times 100\]
  • Crucial for understanding the concentration of different elements within a compound.
  • Helpful in evaluating the purity or concentration of materials used in chemical reactions.
In the example given, mass percent is calculated for barium chloride (\(\text{BaCl}_2\)), revealing its proportion within the initial sample, reflecting the compound's significance in the mixture's overall mass.

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Most popular questions from this chapter

The exact concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) in a solution that is nominally \(6 \%\) \(\mathrm{w} / \mathrm{v} \mathrm{H}_{2} \mathrm{O}_{2}\) is determined by a redox titration using \(\mathrm{MnO}_{4}^{-}\) as the titrant. A \(25-\mathrm{mL}\) aliquot of the sample is transferred to a \(250-\mathrm{mL}\) volumetric flask and diluted to volume with distilled water. A \(25-\mathrm{mL}\) aliquot of the diluted sample is added to an Erlenmeyer flask, diluted with \(200 \mathrm{~mL}\) of distilled water, and acidified with \(20 \mathrm{~mL}\) of \(25 \% \mathrm{v} / \mathrm{v} \mathrm{H}_{2} \mathrm{SO}_{4} .\) The resulting solution is titrated with a standard solution of \(\mathrm{KMnO}_{4}\) until a faint pink color persists for \(30 \mathrm{~s}\). The results are reported as \(\% \mathrm{w} / \mathrm{v} \mathrm{H}_{2} \mathrm{O}_{2}\). (a) Many commercially available solutions of \(\mathrm{H}_{2} \mathrm{O}_{2}\) contain an inorganic or an organic stabilizer to prevent the autodecomposition of the peroxide to \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{O}_{2}\). What effect does the presence of this stabilizer have on the reported \(\% \mathrm{w} / \mathrm{v} \mathrm{H}_{2} \mathrm{O}_{2}\) if it also reacts with \(\mathrm{MnO}_{4}^{-} ?\) (b) Laboratory distilled water often contains traces of dissolved organic material that may react with \(\mathrm{MnO}_{4}^{-}\). Describe a simple method to correct for this potential interference. (c) What modifications to the procedure, if any, are needed if the sample has a nominal concentration of \(30 \% \mathrm{w} / \mathrm{v} \mathrm{H}_{2} \mathrm{O}_{2}\).

The amount of calcium in physiological fluids is determined by a complexometric titration with EDTA. In one such analysis a \(0.100-\mathrm{mL}\) sample of a blood serum is made basic by adding 2 drops of \(\mathrm{NaOH}\) and titrated with \(0.00119 \mathrm{M}\) EDTA, requiring \(0.268 \mathrm{~mL}\) to reach the end point. Report the concentration of calcium in the sample as milligrams Ca per \(100 \mathrm{~mL}\).

The concentration of \(o\) -phthalic acid in an organic solvent, such as \(n\) butanol, is determined by an acid-base titration using aqueous \(\mathrm{NaOH}\) as the titrant. As the titrant is added, the \(o\) -phthalic acid extracts into the aqueous solution where it reacts with the titrant. The titrant is added slowly to allow sufficient time for the extraction to take place. (a) What type of error do you expect if the titration is carried out too quickly? (b) Propose an alternative acid-base titrimetric method that allows for a more rapid determination of the concentration of \(o\) -phthalic acid in \(n\) -butanol.

Commercial washing soda is approximately \(30-40 \% \mathrm{w} / \mathrm{w} \mathrm{Na}_{2} \mathrm{CO}_{3}\). One procedure for the quantitative analysis of washing soda contains the following instructions: Transfer an approximately 4 -g sample of the washing soda to a \(250-\mathrm{mL}\) volumetric flask. Dissolve the sample in about \(100 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) and then dilute to the mark. Using a pipet, transfer a \(25-\mathrm{mL}\) aliquot of this solution to a \(125-\mathrm{mL}\) Erlenmeyer flask and add 25 \(\mathrm{mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) and 2 drops of bromocresol green indicator. Titrate the sample with \(0.1 \mathrm{M} \mathrm{HCl}\) to the indicator's end point. What modifications, if any, are necessary if you want to adapt this procedure to evaluate the purity of commercial \(\mathrm{Na}_{2} \mathrm{CO}_{3}\), that is \(>98 \%\) pure?

The concentration of \(\mathrm{SO}_{2}\) in air is determined by bubbling a sample of air through a trap that contains \(\mathrm{H}_{2} \mathrm{O}_{2} .\) Oxidation of \(\mathrm{SO}_{2}\) by \(\mathrm{H}_{2} \mathrm{O}_{2}\) results in the formation of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), which is then determined by titrating with \(\mathrm{NaOH}\). In a typical analysis, a sample of air is passed through the peroxide trap at a rate of \(12.5 \mathrm{~L} / \mathrm{min}\) for \(60 \mathrm{~min}\) and required \(10.08 \mathrm{~mL}\) of \(0.0244 \mathrm{M} \mathrm{NaOH}\) to reach the phenolphthalein end point. Calculate the \(\mu \mathrm{L} / \mathrm{L} \mathrm{SO}_{2}\) in the sample of air. The density of \(\mathrm{SO}_{2}\) at the temperature of the air sample is \(2.86 \mathrm{mg} / \mathrm{mL}\).
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