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Cumene, a hydrocarbon, is a compound composed only of \(\mathrm{C}\) and \(\mathrm{H}\). It is \(89.94 \%\) carbon, and its molar mass is \(120.2 \mathrm{g} / \mathrm{mol}\). What are the empirical and molecular formulas of cumene?

Short Answer

Expert verified
Empirical formula: \( \text{C}_3\text{H}_4 \); Molecular formula: \( \text{C}_9\text{H}_{12} \).

Step by step solution

01

Calculate Moles of Carbon and Hydrogen

First, remember that the molar mass of carbon \(C\) is approximately \(12.01 \ \mathrm{g/mol}\) and that of hydrogen \(H\) is \(1.008 \ \mathrm{g/mol}\). The problem states that cumene is \(89.94 \%\) carbon, which means in a \(100 \ \mathrm{g}\) sample, \(89.94 \ \mathrm{g}\) is carbon. The rest \((10.06 \ \mathrm{g})\) is hydrogen. Calculate the moles of each: \[ \text{Moles of C} = \frac{89.94}{12.01} \approx 7.49 \] and \[ \text{Moles of H} = \frac{10.06}{1.008} \approx 9.98 \].
02

Determine the Empirical Formula Ratio

After finding moles, the next step is to find the simplest whole number ratio between the number of moles of carbon and hydrogen. Divide each by the smallest number of moles: \[ \text{C : H} = \frac{7.49}{7.49} : \frac{9.98}{7.49} \approx 1 : 1.33 \]. Since \(1.33\) is approximately \(4/3\), multiply the subscripts by \(3\) to get rid of fractions: \( \text{C}_3\text{H}_4 \) is the simplest formula.
03

Calculate the Molar Mass of the Empirical Formula C₃H₄

Now calculate the molar mass of \( \text{C}_3\text{H}_4 \): \[ 3(12.01) + 4(1.008) = 36.03 + 4.032 = 40.062 \ \mathrm{g/mol} \].
04

Determine Molecular Formula from Empirical Formula

To find the molecular formula, compare the molar mass of the empirical formula with the given molar mass of cumene. Divide the molar mass of cumene by the molar mass of the empirical formula: \[ \frac{120.2}{40.062} \approx 3 \]. Thus, multiply the subscripts in the empirical formula \( \text{C}_3\text{H}_4 \) by \(3\): the molecular formula is \( \text{C}_9\text{H}_{12} \).

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Key Concepts

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

Stoichiometry
Stoichiometry is a fundamental concept in chemistry that involves the measurement of the quantities of reactants and products in chemical reactions. It helps chemists understand how substances interact and transform. Stoichiometry calculations are rooted in the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. Therefore, the mass of reactants must equal the mass of products.

In the context of empirical and molecular formulas, stoichiometry enables us to determine the relative amounts of elements in compounds. Here, we are given a breakdown of cumene's composition and need to use stoichiometric principles to find its empirical and molecular formulas. By understanding how to calculate the moles of each element, students can establish ratios that lead to the empirical formula. Subsequently, comparing the empirical formula mass to the given molar mass of the compound reveals how many empirical units make up the molecular formula. This step-by-step calculation exemplifies the stoichiometric prowess needed for chemical composition analysis.

To apply stoichiometry, we need to:
  • Calculate the moles of each component using their mass and molar mass.
  • Establish the simplest whole-number ratio between the elements, resulting in the empirical formula.
  • Determine the molecular formula by comparing the empirical formula mass against the compound's known molar mass.
Molar Mass
Molar mass is essentially the mass of a given substance (chemical element or chemical compound) divided by the amount of substance, which is measured in moles. It's a central concept when dealing with molecule quantities and conversions in chemistry.

For elements, the molar mass is equivalent to the atomic mass found on the periodic table, expressed in grams per mole (g/mol). When calculating the molar mass of compounds, it's crucial to sum the molar masses of all the constituent elements based on their occurrences in the formula. This value helps us convert between mass and moles, which is vital for further stoichiometric calculations.

In our cumene example, the molar mass is provided at 120.2 g/mol, and this is pivotal for determining the compound's molecular formula. By first calculating and then comparing the molar mass of the empirical formula with that of the known molar mass of cumene, we can ascertain how many empirical units are needed for the actual molecular structure. Such comparisons are essential because the empirical formula only represents the simplest ratio of the compound's elemental makeup.
Chemical Composition Analysis
Chemical composition analysis involves determining the elements present in a compound and their respective amounts. This analysis enables chemists to identify substances and understand their structure and properties.

To perform this analysis, especially for unknown compounds, chemists often rely on techniques such as combustion analysis, spectroscopy, and chromatography. These methods help to quickly and accurately determine elemental percentages by mass. For cumene, the percentage composition of carbon was given (89.94%), which facilitated the empirical calculations.

In our exercise, chemical composition analysis begins with assuming a 100 g sample of cumene, translating percentage compositions directly into grams. This simplification aids in calculating the moles of each element present, ultimately leading to the empirical formula. When the molar mass is known, these findings can be further refined to determine the molecular formula, completing the composition analysis. By effectively using both percentage data and molar mass, chemists can pragmatically dissect compounds into clear molecular detail.

Knowing the precise chemical composition equips us to predict how a compound might react under certain conditions and offers insights into its potential applications or hazards.

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Most popular questions from this chapter

A drop of water has a volume of about 0.050 mL. How many molecules of water are in a drop of water? (Assume water has a density of \(1.00 \mathrm{g} / \mathrm{cm}^{3} .\) )

Mass spectrometric analysis showed that there are four isotopes of an unknown element having the following masses and abundances: $$\begin{array}{|c|c|c|c|}\hline \text { Isotope } & \begin{array}{c}\text { Mass } \\\\\text { Number }\end{array} & \begin{array}{c}\text { Isotope } \\\\\text { Mass }\end{array} & \begin{array}{c}\text { Abundance } \\\\(\%)\end{array} \\\\\hline 1 & 136 & 135.9090 & 0.193 \\\\\hline 2 & 138 & 137.9057 & 0.250 \\\\\hline 3 & 140 & 139.9053 & 88.48 \\\\\hline 4 & 142 & 141.9090 & 11.07 \\\\\hline\end{array}$$ Three elements in the periodic table that have atomic weights near these values are lanthanum (La), atomic number \(57,\) atomic weight 138.9055 cerium (Ce), atomic number \(58,\) atomic weight \(140.115 ;\) and praseodymium \((\mathrm{Pr}),\) atomic number \(59,\) atomic weight \(140.9076 .\) Using the data above, calculate the atomic weight, and identify the element if possible.

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