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Chapter 4: Problem 138

In the decomposition of silver(I) carbonate to form metallic silver, carbon dioxide gas, and oxygen gas, (a) one mol of oxygen gas is formed for every 2 mol of carbon dioxide gas; (b) 2 mol of silver metal is formed for every 1 mol of oxygen gas; (c) equal numbers of moles of carbon dioxide and oxygen gases are produced; (d) the same number of moles of silver metal are formed as of the silver(I) carbonate decomposed.

Short Answer

Expert verified
The balanced chemical reaction for the decomposition of silver(I) carbonate is: \(2Ag_2CO_3 \rightarrow 4Ag + 2CO_2 + 2O_2\)

Step by step solution

01

Identify the given relationships

From the exercise, the given relationships are: (a) one mol of oxygen gas is formed for every 2 mol of carbon dioxide gas, (b) 2 mol of silver metal is formed for every 1 mol of oxygen gas, (c) equal numbers of moles of carbon dioxide and oxygen gases are produced, (d) the same number of moles of silver metal are formed as of the silver(I) carbonate decomposed.
02

Write the unbalanced chemical reaction

The general unbalanced reaction for the decomposition of silver(I) carbonate is written as: \( Ag_2CO_3 \rightarrow Ag + CO_2 + O_2 \)
03

Balance the chemical reaction

Considering the given relationships, the balanced reaction becomes: \( 2Ag_2CO_3 \rightarrow 4Ag + 2CO_2 + 2O_2 \) Here, for every 2 moles of silver(I) carbonate that decomposes, 4 moles of silver, 2 moles of carbon dioxide and 2 moles of oxygen are produced. This satisfies all the given conditions.

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Most popular questions from this chapter

Chalkboard chalk is made from calcium carbonate and calcium sulfate, with minor impurities such as \(\mathrm{SiO}_{2} .\) Only the \(\mathrm{CaCO}_{3}\) reacts with dilute \(\mathrm{HCl}(\mathrm{aq})\) What is the mass percent \(\mathrm{CaCO}_{3}\) in a piece of chalk if a 3.28 -g sample yields \(0.981 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}) ?\) $$\begin{aligned} \mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) & \longrightarrow \mathrm{CaCl}_{2}(\mathrm{aq}) +\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g}) \end{aligned}$$

An essentially \(100 \%\) yield is necessary for a chemical reaction used to analyze a compound, but it is almost never expected for a reaction that is used to synthesize a compound. Explain this difference.

It is often difficult to determine the concentration of a species in solution, particularly if it is a biological species that takes part in complex reaction pathways. One way to do this is through a dilution experiment with labeled molecules. Instead of molecules, however, we will use fish. An angler wants to know the number of fish in a particular pond, and so puts an indelible mark on 100 fish and adds them to the pond's existing population. After waiting for the fish to spread throughout the pond, the angler starts fishing, eventually catching 18 fish. Of these, five are marked. What is the total number of fish in the pond?

Baking soda, \(\mathrm{NaHCO}_{3}\), is made from soda ash, a common name for sodium carbonate. The soda ash is obtained in two ways. It can be manufactured in a process in which carbon dioxide, ammonia, sodium chloride, and water are the starting materials. Alternatively, it is mined as a mineral called trona (left photo). Whether the soda ash is mined or manufactured, it is dissolved in water and carbon dioxide is bubbled through the solution. Sodium bicarbonate precipitates from the solution. As a chemical analyst you are presented with two samples of sodium bicarbonate-one from the manufacturing process and the other derived from trona. You are asked to determine which is purer and are told that the impurity is sodium carbonate. You decide to treat the samples with just sufficient hydrochloric acid to convert all the sodium carbonate and bicarbonate to sodium chloride, carbon dioxide, and water. You then precipitate silver chloride in the reaction of sodium chloride with silver nitrate. A \(6.93 \mathrm{g}\) sample of baking soda derived from trona gave \(11.89 \mathrm{g}\) of silver chloride. A \(6.78 \mathrm{g}\) sample from manufactured sodium carbonate gave \(11.77 \mathrm{g}\) of silver chloride. Which sample is purer, that is, which has the greater mass percent \(\mathrm{NaHCO}_{3} ?\)

Iron ore is impure \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) When \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is heated with an excess of carbon (coke), metallic iron and carbon monoxide gas are produced. From a sample of ore weighing \(938 \mathrm{kg}, 523 \mathrm{kg}\) of pure iron is obtained. What is the mass percent \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) by mass, in the ore sample, assuming that none of the impurities contain Fe?
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