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Chapter 9: Problem 60

A \(0.1093-\mathrm{g}\) sample of impure \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is analyzed by the Volhard method. After adding \(50.00 \mathrm{~mL}\) of \(0.06911 \mathrm{M} \mathrm{AgNO}_{3},\) the sample is back titrated with \(0.05781 \mathrm{M} \mathrm{KSCN}\), requiring \(27.36 \mathrm{~mL}\) to reach the end point. Report the purity of the \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) sample.

Short Answer

Expert verified
The purity of the Na2CO3 sample is 90.75%.

Step by step solution

01

Calculate Moles of AgNO3 Added

First, determine the total moles of AgNO3 that were initially added to the sample. Use the formula:\[moles = Molarity \times Volume (L)\]Thus,\[moles_{AgNO3} = 0.06911 \, M \times 0.05000 \, L = 0.0034555 \, ext{mol}\]
02

Calculate Moles of KSCN Used

Determine the number of moles of KSCN used in the back titration. This can be calculated using the formula:\[moles = Molarity \times Volume (L)\]Hence,\[moles_{KSCN} = 0.05781 \, M \times 0.02736 \, L = 0.001582 \, ext{mol}\]
03

Calculate Moles of Excess AgNO3

The moles of KSCN used give the moles of excess AgNO3 because the KSCN reacts one-to-one with the excess silver nitrate. Therefore, the moles of excess AgNO3 are:\[moles_{excess \, AgNO3} = 0.001582 \, ext{mol}\]
04

Calculate Moles of AgNO3 That Reacted With Na2CO3

Subtract the moles of excess AgNO3 from the initial moles to find the moles of AgNO3 that reacted with Na2CO3:\[moles_{AgNO3 \, reacted} = 0.0034555 \, ext{mol} - 0.001582 \, ext{mol} = 0.0018735 \, ext{mol}\]
05

Relate Moles of AgNO3 to Na2CO3

The reaction between Na2CO3 and AgNO3 is:\[\text{Na2CO3} + 2\text{AgNO3} \rightarrow 2\text{NaNO3} + \text{Ag2CO3}\]This implies that 1 mole of Na2CO3 reacts with 2 moles of AgNO3. Thus, the moles of Na2CO3 in the sample is:\[moles_{Na2CO3} = \frac{0.0018735}{2} = 0.00093675 \, ext{mol}\]
06

Calculate Mass of Na2CO3 in Sample

Calculate the mass of Na2CO3 in the impure sample using the molar mass of Na2CO3 (105.99 g/mol):\[mass_{Na2CO3} = 0.00093675 \, ext{mol} \times 105.99 \, \frac{g}{mol} = 0.09919 \, ext{g}\]
07

Determine Purity of Na2CO3 Sample

The purity of the sample is given by the ratio of the mass of pure Na2CO3 to the mass of the impure sample, multiplied by 100%:\[\text{Purity \%} = \left(\frac{0.09919 \, \text{g}}{0.1093 \, \text{g}} \right) \times 100\% = 90.75\%\]

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Key Concepts

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

Purity Analysis
Purity analysis is a fundamental task in analytical chemistry. It involves measuring the proportion of a specified component in a mixture or sample. In this context, it empowers us to determine how much of the compound we are interested in is present compared to impurities.

Performing purity analysis is vital for various reasons:
  • Ensures quality control in manufacturing processes.
  • Determines the suitability of a chemical sample for specific applications.
  • Assists in regulatory compliance, particularly in pharmaceuticals and food industries.
The analysis is carried out by comparing the mass of the pure substance, calculated from a chemical reaction, to the total mass of the sample. This process's results are often provided as a percentage, indicating how pure the sample really is.
Back Titration
Back titration is an ingenious analytical technique used especially when the reactants involved or their products do not give a sharp endpoint. By allowing a reaction to partially occur and then titrating the unreacted excess, practitioners can determine the amount of substance originally present.

In a typical back titration:
  • First, an excess of titrant is added to the analyte.
  • The remaining, unreacted titrant is then titrated with a second titrant.
  • The difference helps determine the amount of analyte in question.
This method is particularly useful when dealing with substances that are slow to react or in reactions where the endpoint is challenging to detect directly. By using a back titration, uncertainty in the directly measured quantity can be reduced, increasing the reliability of quantitative analysis.
Sodium Carbonate (Na2CO3)
Sodium carbonate, known commonly as washing soda or soda ash, is a highly applicable chemical compound in various industries. With the molecular formula Na2CO3, it is an anhydrous, white crystalline solid often used in domestic and industrial settings.

Applications of Na2CO3 include:
  • Glass manufacturing, by providing sodium to the manufacture.
  • Water softening, as it removes calcium and magnesium ions.
  • Cleaning agents, due to its alkaline nature to neutralize acidic stains.
Moreover, sodium carbonate is used in scientific laboratories for standard solution preparation due to its relatively stable and non-hygroscopic nature, making it ideal for purity analysis experiments.
Analytical Chemistry
Analytical chemistry is the branch of chemistry concerned with the study of material samples to understand their composition and quantify each component. It's a crucial science that drives innovation in environmental monitoring, disease diagnostics, and more.

Core functions of analytical chemistry include:
  • Qualitative analysis, identifying what substances are present.
  • Quantitative analysis, measuring how much of each substance is present.
  • Method development, creating new experimental procedures.
In the context of the Volhard method applied to an impure Na2CO3 sample, analytical chemistry allows for rigorous and quantitative evaluation of purity through intricate reaction mechanisms and precise measurements.

By understanding these core concepts, students and scientists harness the power of analytical techniques to refine, understand, and innovate within the realms of chemistry and applied sciences.

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Most popular questions from this chapter

An acid-base titration can be used to determine an analyte's equivalent weight, but it can not be used to determine its formula weight. Explain why.

After removing the membranes from an eggshell, the shell is dried and its mass recorded as \(5.613 \mathrm{~g} .\) The eggshell is transferred to a \(250-\mathrm{mL}\) beaker and dissolved in \(25 \mathrm{~mL}\) of \(6 \mathrm{M}\) HCl. After filtering, the solution that contains the dissolved eggshell is diluted to \(250 \mathrm{~mL}\) in a volumetric flask. A \(10.00-\mathrm{mL}\) aliquot is placed in a \(125-\mathrm{mL}\) Erlenmeyer flask and buffered to a \(\mathrm{pH}\) of 10 . Titrating with \(0.04988 \mathrm{M}\) EDTA requires \(44.11 \mathrm{~mL}\) to reach the end point. Determine the amount of calcium in the eggshell as \(\% \mathrm{w} / \mathrm{w} \mathrm{CaCO}_{3}\).

Before the introduction of EDTA most complexation titrations used \(\mathrm{Ag}^{+}\) or \(\mathrm{CN}^{-}\) as the titrant. The analysis for \(\mathrm{Cd}^{2+},\) for example, was accomplished indirectly by adding an excess of \(\mathrm{KCN}\) to form \(\mathrm{Cd}(\mathrm{CN})_{4}^{2-}\), and back titrating the excess \(\mathrm{CN}^{-}\) with \(\mathrm{Ag}^{+},\) forming \(\mathrm{Ag}(\mathrm{CN})_{2}^{-} .\) In one such analysis a \(0.3000-\mathrm{g}\) sample of an ore is dissolved and treated with \(20.00 \mathrm{~mL}\) of \(0.5000 \mathrm{M} \mathrm{KCN}\). The excess \(\mathrm{CN}^{-}\) requires \(13.98 \mathrm{~mL}\) of \(0.1518 \mathrm{M} \mathrm{AgNO}_{3}\) to reach the end point. Determine the \(\% \mathrm{w} / \mathrm{w}\) Cd in the ore.

The concentration of \(\mathrm{CO}\) in air is determined by passing a known volume of air through a tube that contains \(\mathrm{I}_{2} \mathrm{O}_{5}\), forming \(\mathrm{CO}_{2}\) and \(\mathrm{I}_{2}\). The \(\mathrm{I}_{2}\) is removed from the tube by distilling it into a solution that contains an excess of \(\mathrm{KI}\), producing \(\mathrm{I}_{3}^{-}\). The \(\mathrm{I}_{3}^{-}\) is titrated with a standard solution of \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\). In a typical analysis a 4.79 - \(\mathrm{L}\) sample of air is sampled as described here, requiring \(7.17 \mathrm{~mL}\) of \(0.00329 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) to reach the end point. If the air has a density of \(1.23 \times 10^{-3} \mathrm{~g} / \mathrm{mL},\) determine the parts per million CO in the air.

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 \(100 \mathrm{~mL}\).
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