Calculate the empirical formula of each compound from the...

Calculate the empirical formula of each compound from the percent compositions given: (a) $64.1 \% \mathrm{Cu}, 35.9 \% \mathrm{Cl}$ (b) $47.2 \% \mathrm{Cu}, 52.8 \% \mathrm{Cl}$ (c) $51.9 \% \mathrm{Cr}, 48.1 \% \mathrm{~S}$ (d) $55.3 \% \mathrm{~K}, 14.6 \% \mathrm{P}, 30.1 \% \mathrm{O}$ (e) $38.9 \% \mathrm{Ba}, 29.4 \% \mathrm{Cr}, 31.7 \% \mathrm{O}$ (f) $3.99 \% \mathrm{P}, 82.3 \% \mathrm{Br}, 13.7 \% \mathrm{Cl}$

Calculate the empirical formula of each compound from the percent compositions given:
(a) $64.1 \% \mathrm{Cu}, 35.9 \% \mathrm{Cl}$
(b) $47.2 \% \mathrm{Cu}, 52.8 \% \mathrm{Cl}$
(c) $51.9 \% \mathrm{Cr}, 48.1 \% \mathrm{~S}$
(d) $55.3 \% \mathrm{~K}, 14.6 \% \mathrm{P}, 30.1 \% \mathrm{O}$
(e) $38.9 \% \mathrm{Ba}, 29.4 \% \mathrm{Cr}, 31.7 \% \mathrm{O}$
(f) $3.99 \% \mathrm{P}, 82.3 \% \mathrm{Br}, 13.7 \% \mathrm{Cl}$

Key Concepts

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. It provides the relative amounts of each element present and serves as the starting point for determining the compound's empirical formula. This concept is pivotal in analytical chemistry and stoichiometry, where mass percentages are used to infer the proportions of elements in a sample.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. It does not necessarily indicate the actual number of atoms present, but it describes the basic building block of the compound's composition. Determining the empirical formula is a fundamental aspect of chemical analysis and synthesis, converting percent composition data into a molecular representation.

Conversion from Mass to Moles

Converting mass to moles is a critical step in determining the empirical formula. Since percentage composition data is given in mass percent, it is necessary to convert these values into moles by using the atomic masses of the elements. This process allows for a direct comparison between different elements based on the number of particles rather than their mass.

Mole Ratio Determination

After obtaining the number of moles for each element, the next step involves finding the simplest ratio among them. This is done by dividing each molar amount by the smallest number of moles present. The resulting ratios, if not whole numbers, are multiplied by the appropriate factor to convert them into whole numbers, which then directly inform the empirical formula.

Stoichiometric Analysis

Stoichiometric analysis involves using the quantitative relationships between reactants and products in chemical reactions. In the context of empirical formula determination, stoichiometry is used to relate the mass of each element to its mole quantity and to simplify these quantities into a coherent, balanced formula that reflects the compound's elemental makeup.

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