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A 2.46-gram sample of copper metal is reacted completely with chlorine gas to produce \(5.22\) grams of copper chloride. Determine the empirical formula of this chloride.

Short Answer

Expert verified
The empirical formula is \(\text{CuCl}_2\).

Step by step solution

01

Determine Mass of Chlorine

To find the mass of chlorine, subtract the mass of copper from the mass of copper chloride: \( 5.22\text{ g} - 2.46\text{ g} = 2.76\text{ g} \).
02

Calculate Moles of Copper

The molar mass of copper is approximately \(63.55 \text{ g/mol}\). Calculate moles of copper: \( \frac{2.46\text{ g}}{63.55\text{ g/mol}} = 0.0387\text{ mol}\).
03

Calculate Moles of Chlorine

The molar mass of chlorine is approximately \(35.45 \text{ g/mol}\). Calculate moles of chlorine: \( \frac{2.76\text{ g}}{35.45\text{ g/mol}} = 0.0779\text{ mol}\).
04

Determine the Molar Ratio

Find the simplest whole number ratio of copper to chlorine by dividing both mole amounts by the smallest number of moles: \( \frac{0.0387}{0.0387} = 1\) for copper and \( \frac{0.0779}{0.0387} = 2.01\) for chlorine.
05

Conclude Empirical Formula

Since the ratio of copper to chlorine simplifies closely to \(1:2\), the empirical formula of the compound is \(\text{CuCl}_2\).

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Key Concepts

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

Stoichiometry
Stoichiometry is a vital concept in chemistry that involves the calculation of reactants and products in chemical reactions. It helps us understand the relationship between the amounts of substances used and produced during chemical reactions. In exercises like determining an empirical formula, stoichiometry provides the foundation to relate amounts in grams to amounts in moles, using known molar masses.

These calculations typically include:
  • Mass-to-mole conversions: Starting with the mass of a substance, we convert it to moles.
  • Mole ratios: Based on the balanced chemical equation or experiment, a mole ratio is determined and used to find the relative quantities of reactants and products.
Through this approach, you can efficiently determine empirical formulas by establishing the simplest ratio of elements within a compound.
Understanding stoichiometry makes it easier to solve complex chemistry problems, like calculating the empirical formula from given masses.
Moles Calculation
Calculating moles is a cornerstone of chemistry that enables us to translate between mass and quantity of particles (atoms or molecules). The concept of moles involves using the molar mass, which is the mass of one mole of a substance. This is expressed in grams per mole (g/mol). Knowing the molar mass allows us to convert mass in grams to moles using a simple division.

For example, in the original exercise, we calculated the moles of copper and chlorine:
  • For copper: with a given mass of 2.46 g and a molar mass of 63.55 g/mol, the computation is \( \frac{2.46\text{ g}}{63.55\text{ g/mol}} = 0.0387\text{ mol}\).
  • For chlorine: using a mass of 2.76 g and a molar mass of 35.45 g/mol, the result is \( \frac{2.76\text{ g}}{35.45\text{ g/mol}} = 0.0779\text{ mol}\).
These calculations set the stage for determining the empirical formula by providing the necessary mole quantities for comparison.
Molar Mass
The concept of molar mass is crucial when dealing with chemical reactions and calculations. Molar mass provides the bridge between the mass of a substance and the amount of particles it contains, measured in moles. It is expressed in grams per mole (g/mol) and is specific to each element or compound.

To find the molar mass, one needs to know the atomic masses of the elements involved, usually found on the periodic table. For instance, in the exercise provided, the molar mass of copper is approximately 63.55 g/mol, while for chlorine, it's about 35.45 g/mol.

When solving for empirical formulas, having accurate molar masses enables you to precisely calculate the number of moles from a given mass. This step is fundamental in converting empirical quantities into molar terms, which are then used to find the simplest whole number ratio for the formula. It allows chemists to gain insights into the makeup of compounds, guiding further chemical analyses and synthesis.

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Most popular questions from this chapter

The chemical N,N'-diethyl- \(m\) -toluamide, commonly known as DEET, was developed by the U.S. Army following World War II as an insect repellent for use in jungle warfare. DEET works by blocking insect receptors used to locate hosts. The chemical formula of DEET is \(\mathrm{C}_{12} \mathrm{H}_{17} \mathrm{NO} .\) Determine the mass percentage of each of the elements in DEET to four significant figures and show that the sum of these mass percentages totals one hundred percent.

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Why is it not possible for a reaction to have a percentage yield of the desired product greater than \(100 \%\) (what law is this in violation of)? What is the most likely explanation for a percentage yield measured in the laboratory that is in excess of \(100 \%\) ?

A class of compounds called sodium metaphosphates was used as additives to detergents to improve cleaning ability. One of them has a molecular mass of 612\. Chemical analysis shows that this sodium metaphosphate consists of \(22.5 \%\) sodium, \(30.4 \%\) phosphorus, and \(47.1 \%\) oxygen by mass. Determine the molecular formula of this compound.

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