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An organic compound was found to contain only \(\mathrm{C}, \mathrm{H}\), and Cl. When a \(1.50-g\) sample of the compound was completely combusted in air, \(3.52 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) was formed. In a separate experiment the chlorine in a \(1.00-\mathrm{g}\) sample of the compound was converted to \(1.27 \mathrm{~g}\) of \(\mathrm{AgCl}\). Determine the empirical formula of the compound.

Short Answer

Expert verified
The empirical formula of the organic compound containing C, H, and Cl is \(C_{2}H_{5}Cl\).

Step by step solution

01

Calculate moles of carbon from COâ‚‚ mass.

To find the moles of carbon in the compound, we will use the mass of CO₂ formed upon combustion. The molar mass of CO₂ is (12.01 g/mol for C) + (2 × 16.00 g/mol for O) = 44.01 g/mol. Using the given mass of CO₂ (3.52 g), we can find the moles of carbon as: moles of carbon in CO₂ = (mass of CO₂) / (molar mass of CO₂) moles of carbon = \( \frac{3.52\,\mathrm{g}}{44.01\,\mathrm{g/mol}} \)
02

Calculate the moles of chlorine from AgCl mass.

To find the moles of chlorine in the compound, we will use the mass of AgCl formed when reacting with silver. The molar mass of AgCl is (107.87 g/mol for Ag) + (35.45 g/mol for Cl) = 143.32 g/mol. Using the given mass of AgCl (1.27 g), we can find the moles of chlorine as: moles of chlorine in AgCl = (mass of AgCl) / (molar mass of AgCl) moles of chlorine = \( \frac{1.27\,\mathrm{g}}{143.32\,\mathrm{g/mol}} \)
03

Calculate the mass of hydrogen in the compound.

We can calculate the mass of hydrogen in the 1.50-g sample of the compound using the mass of carbon and chlorine. From the moles of carbon obtained in step 1, we can find the mass of carbon in the sample as: mass of carbon = moles of carbon × molar mass of C From the moles of chlorine obtained in step 2, we can find the mass of chlorine in the sample as: mass of chlorine = moles of chlorine × molar mass of Cl Now, we can calculate the mass of hydrogen as: mass of hydrogen = mass of sample - (mass of carbon + mass of chlorine)
04

Calculate the moles of hydrogen.

Next, we need to find the moles of hydrogen in the compound. We can do this by dividing the mass of hydrogen calculated in step 3 by the molar mass of hydrogen (1.01 g/mol): moles of hydrogen = mass of hydrogen / molar mass of H
05

Determine the empirical formula.

Finally, we need to determine the ratio of C, H, and Cl in the compound. To do this, divide all the moles obtained in steps 1, 2, and 4 by the smallest mole value. This will give us a whole number ratio of the elements present in the compound. After finding the value of the ratio, we can write the empirical formula of the compound.

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Key Concepts

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

Stoichiometry
The field of stoichiometry is a fundamental aspect of chemistry that involves determining the amounts of substances consumed and produced in chemical reactions. It is essentially the study of the quantitative relationships between reactants and products in a chemical equation.

Stoichiometry is crucial when working to find the empirical formula of a compound, as it provides a clear guide to understand the ratios of different atoms within a molecule. This is done by comparing the number of moles of each element, which is a measure of quantity in chemistry. The process requires precise calculations to ensure accuracy and to reflect the true proportions of the elements.
Combustion Analysis
Combustion analysis is an experimental procedure used in chemistry to determine the composition of organic compounds. During this process, a known mass of a compound is burned in excess oxygen, and the masses of the resulting carbon dioxide and water are measured. These measurements then allow chemists to calculate the amount of carbon and hydrogen in the original compound.

When the compound also contains elements like chlorine, additional steps are necessary such as treating with silver to precipitate out silver chloride, AgCl, which can then be weighed to find the mass -- and therefore the moles -- of chlorine. This systematic approach enables the determination of the empirical formula by highlighting the proportional amounts of each element in the sample.
Mole Concept
The mole concept is an essential principle in chemistry that defines the amount of substance. One mole contains Avogadro's number of particles, which is approximately 6.022 x 1023. This concept is pivotal when dealing with the microscopic world of atoms and molecules, providing a bridge between the mass of a substance and the number of its constituent particles.

Moles allow comparisons of elements and compounds on a common scale and serve as a critical intermediary in stoichiometry. They offer a way to convert between the mass of a substance (in grams) and the number of its particles (atoms, molecules, ions, etc.), which is particularly handy when determining ratios of elements within compounds.
Molar Mass
The molar mass is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is directly related to the molecular weight of a compound, which is the sum of the atomic weights of all atoms present in the molecule. The atomic weights are found on the periodic table and represent the average mass of an element’s atoms.

In empirical formula determination, the molar mass enables the conversion of masses from experiments (like the mass of COâ‚‚ produced in combustion or the mass of AgCl formed) to moles. This step is fundamental to proportionally compare elements within a compound, leading to the ratio of atoms in the empirical formula. For instance, the molar mass of carbon dioxide (COâ‚‚) is central to finding the number of moles of carbon when a sample is combusted.

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Most popular questions from this chapter

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, which are principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%)\). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NOx" gases. In 2004, the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{\mathrm{x}}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane, and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of 500 grams of octane.

Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for the reaction. (b) How many grams of calcium hydride are needed to form \(8.500 \mathrm{~g}\) of hydrogen?

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\), \(8.80 \% \mathrm{H}\), and \(15.51 \%\) O by mass, and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H}\), and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\). (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \% \mathrm{C}, 7.1 \% \mathrm{H}, 26.2 \% \mathrm{O}\), and \(7.7 \% \mathrm{~N}\) by mass; its \(\mathrm{MW}\) is about \(180 \mathrm{amu}\).

(a) What is the mass, in grams, of \(0.0714 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(8.776 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(6.52 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{\mathrm{g}} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{8}\) ) if \(0.05570\) mol weighs \(15.86 \mathrm{~g}\) ?

Automotive air bags inflate when sodium azide, \(\mathrm{NaN}_{3}\). rapidly decomposes to its component elements: $$ 2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(\mathrm{s})+3 \mathrm{~N}_{2}(g) $$ (a) How many moles of \(\mathrm{N}_{2}\) are produced by the decomposition of \(1.50 \mathrm{~mol}\) of \(\mathrm{Na} \mathrm{N}_{3}\) ? (b) How many grams of \(\mathrm{NaN}_{3}\) are required to form \(10.0 \mathrm{~g}\) of nitrogen gas? (c) How many grams of \(\mathrm{NaN}_{3}\) are required to produce \(10.0 \mathrm{ft}^{3}\) of nitrogen gas, about the size of an automotive air bag, if the gas has a density of \(1.25 \mathrm{~g} / \mathrm{L} ?\)

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