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Chapter 7: Problem 56

A sample of an iron-containing compound is \(22.0 \%\) iron, \(50.2 \%\) oxygen, and \(27.8 \%\) chlorine by mass. What is the empirical formula of this compound?

Short Answer

Expert verified
The empirical formula of the iron-containing compound is FeO8Cl2.

Step by step solution

01

Convert mass percentages to grams

Consider a 100g sample of the compound, since this will make working with the mass percentages easier. The masses of the elements are: - Iron (Fe): \(22.0 \%\) of 100g \(\implies\) 22.0g - Oxygen (O): \(50.2 \%\) of 100g \(\implies\) 50.2g - Chlorine (Cl):\(27.8 \%\) of 100g \(\implies\) 27.8g
02

Convert grams to moles for each element

Using the molar mass of each element, convert the masses obtained in step 1 to moles: - Moles of Fe: \(\frac{22.0}{55.85 \text{ g/mol}} = 0.3938 \text{ mol}\) - Moles of O: \(\frac{50.2}{16.00 \text{ g/mol}} = 3.1375 \text{ mol}\) - Moles of Cl: \(\frac{27.8}{35.45 \text{ g/mol}} = 0.7844 \text{ mol}\)
03

Find the simplest whole number ratio of moles

Determine the smallest value of moles found in step 2: \(\text{min}(0.3938, 3.1375, 0.7844) = 0.3938\) Now divide the moles of each element by this smallest value to find the ratio: - Ratio of Fe: \(\frac{0.3938}{0.3938} = 1\) - Ratio of O: \(\frac{3.1375}{0.3938} \approx 7.97 \approx 8\) - Ratio of Cl: \(\frac{0.7844}{0.3938} \approx 1.99 \approx 2\)
04

Write the empirical formula

Based on the whole number ratios found in step 3, the empirical formula of the iron-containing compound is FeO\(_8\)Cl\(_2\).

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Most popular questions from this chapter

When \(\mathrm{NaHCO}_{3}\) is heated above \(270^{\circ} \mathrm{C},\) it decomposes to \(\mathrm{Na}_{2} \mathrm{CO}_{3}(s), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{CO}_{2}(g)\) a. Write a balanced chemical equation for the decomposition reaction. b. Calculate the mass of \(\mathrm{CO}_{2}\) produced from the decomposition of \(25.0 \mathrm{g} \mathrm{NaHCO}_{3}.\)

Sometimes the composition of a compound is expressed in units of mol \(\%\) or atom \(\% .\) Are the values of these parameters likely to be the same or different for a given compound?

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Organic Compounds in Space The following compounds have been detected in space. Which contains the greatest percentage of carbon by mass? a. naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\) b. chrysene, \(\mathrm{C}_{18} \mathrm{H}_{12}\) c. pentacene, \(\mathrm{C}_{22} \mathrm{H}_{14}\) d. pyrene, \(C_{16} H_{10}\)

Black Powder Gunpowder, known also as black powder, is generally thought to have been invented by the Chinese in the 9 th century. The first description in English was given by Roger Bacon in the 13 th century. The basic formulation has not changed since then: \(40 \%\) potassium nitrate, \(30 \%\) carbon, and \(30 \%\) sulfur by weight. The products of the reaction that provide the explosive force when the powder is ignited are three gases: carbon monoxide, carbon dioxide, and nitrogen. An additional product is potassium sulfite. Consider a sample of \(100 \mathrm{g}\) of black powder. a. Which reagent is limiting? b. How much of each of the reagents in excess is left over after the explosion takes place?
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