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Chapter 4: Problem 23

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?

Short Answer

Expert verified
The mass percent of \(Fe_2O_3\) in the ore sample is about 72.39%.

Step by step solution

01

Calculate the amount of \(Fe_2O_3\) that could form from 523 kg Fe

Given the molar mass of Fe is about 55.85 g/mol and \(Fe_2O_3\) is about 159.69 g/mol, the moles of Fe and \(Fe_2O_3\) can be calculated respectively with the formula: \( \text{No.of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). After calculating the moles of Fe, multiple it by 1.5 to get the moles of \(Fe_2O_3\), because 2 moles of Fe produce 1 mole of \(Fe_2O_3\). Lastly, convert the moles of \(Fe_2O_3\) back to mass in kg.
02

Calculate mass percent of \(Fe_2O_3\)

Next, calculate the mass percent of \(Fe_2O_3\) by dividing the mass of \(Fe_2O_3\) obtained in step 1 by the total mass of the ore sample (938 kg), and then multiply by 100. The result is the mass percent of \(Fe_2O_3\) in the ore sample.

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Most popular questions from this chapter

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 \(\mathrm{NaHCO}_{3} ?\)

In your own words, define or explain these terms or symbols. (a) \(\stackrel{\Delta}{\longrightarrow}\) (b) (aq) (c) stoichiometric coefficient (d) overall equation

A method of lowering the concentration of \(\mathrm{HCl}(\mathrm{aq})\) is to allow the solution to react with a small quantity of Mg. How many milligrams of Mg must be added to \(250.0 \mathrm{mL}\) of \(1.023 \mathrm{M} \mathrm{HCl}\) to reduce the solution concentration to exactly \(1.000 \mathrm{M} \mathrm{HCl} ?\) $$ \mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$

What are the molarities of the following solutes? (a) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) if \(150.0 \mathrm{g}\) is dissolved per \(250.0 \mathrm{mL}\) of water solution (b) urea, \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) if \(98.3 \mathrm{mg}\) of the \(97.9 \%\) pure solid is dissolved in \(5.00 \mathrm{mL}\) of aqueous solution (c) methanol, \(\mathrm{CH}_{3} \mathrm{OH},(d=0.792 \mathrm{g} / \mathrm{mL})\) if \(125.0 \mathrm{mL}\) is dissolved in enough water to make 15.0 L of solution

Briefly describe (a) balancing a chemical equation; (b) preparing a solution by dilution; (c) determining the limiting reactant in a reaction.
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