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Chapter 9: Problem 113

A compound composed of \(6.7 \% \mathrm{H}, 40.0 \% \mathrm{C},\) and $53.3 \% \mathrm{O}\( has a molar mass of approximately \)60 \mathrm{~g} / \mathrm{mol}$. (a) What is the molecular formula of the compound? (b) What is its Lewis structure if the two \(\mathrm{O}\) are bonded to \(\mathrm{C} ?\) (c) What is the geometry and hybridization of the \(\mathrm{C}\) atom that is bonded to $2 \mathrm{O}\( atoms? (d) How many \)\sigma\( and how many \)\pi$ bonds are there in the molecule?

Short Answer

Expert verified
The molecular formula of the compound is C2H4O2. Its Lewis structure has a central carbon (C2) double bonded to two oxygen atoms and connected to another carbon (C3) which is bonded to three hydrogen atoms. The geometry around C2 is linear with sp hybridization, and the geometry around C3 is tetrahedral with sp3 hybridization. The molecule has a total of 6 σ bonds and 2 π bonds.

Step by step solution

01

Calculate the Empirical Formula.

First, we'll use the given percentage composition to find the empirical formula. We will consider having 100 grams of the compound and calculate the moles of each element in it. For Hydrogen: \[6.7~g \left(\dfrac{1~mole}{1~g}\right) = 6.7~moles\] For Carbon: \[40.0~g \left(\dfrac{1~mole}{12.01~g}\right) \approx 3.3~moles\] For Oxygen: \[53.3~g \left(\dfrac{1~mole}{16.00~g}\right) \approx 3.3~moles\] Now, let's divide the moles of each element by their lowest value to find the ratio: \[C : H : O = 3.3 : 6.7 : 3.3\] Divide by 3.3: \[C : H : O = 1 : 2 : 1\] The empirical formula is CH2O.
02

Calculate the Molecular Formula.

Now, let's use the empirical formula and its molar mass to find the molecular formula. First, find the empirical formula molar mass. For CH2O: Molar Mass = 12.01 + 2 (1) + 16 = 30 g/mol Given that the molar mass of the compound is approximately 60 g/mol: Molecular Formula = Empirical Formula × n (where n is an integer) Let's find the value of n: \[n = \dfrac{60}{30} = 2\] Now, multiply the empirical formula by n to get the molecular formula: C(2)H(2×2)O(2) = C2H4O2
03

Draw the Lewis Structure.

Based on the given information, the two oxygen atoms are bonded to a central carbon atom. The Lewis structure for this molecule can be drawn as: O=C(2) || O=C ! H ! H /(3) C ! H ! H Here, the numbers inside the parentheses indicate the carbon atom number. Double bonds are shown with two lines.
04

Geometry and Hybridization of Carbon Atoms.

The central carbon atom (C2) is double bonded to two oxygen atoms. This arrangement suggests a linear geometry around this carbon. The hybridization for this carbon is sp, as it has two electron groups consisting of two double bonds. The geometry around carbon atom C3 is tetrahedral with a hybridization of sp3.
05

Determine the Number of σ and π Bonds.

To complete the exercise, we'll count the number of σ and π bonds in the molecule. - Carbon atom 2 (C2) has two σ bonds (one each to oxygen atoms) and two π bonds (one each in the double bonds with oxygen atoms). - Carbon atom 3 (C3) has four σ bonds (to carbon atom 2 and three hydrogen atoms). Total: 6 σ bonds and 2 π bonds.

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Most popular questions from this chapter

(a) Write a single Lewis structure for \(\mathrm{N}_{2} \mathrm{O},\) and determine the hybridization of the central \(\mathrm{N}\) atom. (b) Are there other possible Lewis structures for the molecule? (c) Would you expect \(\mathrm{N}_{2} \mathrm{O}\) to exhibit delocalized \(\pi\) bonding?

Methyl isocyanate, \(\mathrm{CH}_{3} \mathrm{NCO},\) was made infamous in 1984 when an accidental leakage of this compound from a storage tank in Bhopal, India, resulted in the deaths of about 3800 people and severe and lasting injury to many thousands more. (a) Draw a Lewis structure for methyl isocyanate. (b) Draw a ball-and-stick model of the structure, including estimates of all the bond angles in the compound. (c) Predict all the bond distances in the molecule. (d) Do you predict that the molecule will have a dipole moment? Explain.

In ozone, \(\mathrm{O}_{3}\), the two oxygen atoms on the ends of the molecule are equivalent to one another. (a) What is the best choice of hybridization scheme for the atoms of ozone? (b) For one of the resonance forms of ozone, which of the orbitals are used to make bonds and which are used to hold nonbonding pairs of electrons? (c) Which of the orbitals can be used to delocalize the \(\pi\) electrons? (d) How many electrons are delocalized in the \(\pi\) system of ozone?

How would you expect the extent of overlap of the bonding atomic orbitals to vary in the series IF, ICl, IBr, and \(I_{2}\) ? Explain your answer.

What is the distinction between a bond dipole and a molecular dipole moment?
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