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Chapter 3: Problem 89

A compound contains \(47.08 \%\) carbon, \(6.59 \%\) hydrogen, and \(46.33 \%\) chlorine by mass; the molar mass of the compound is \(153 \mathrm{~g} / \mathrm{mol}\). What are the empirical and molecular formulas of the compound?

Short Answer

Expert verified
The compound contains carbon, hydrogen, and chlorine in the approximate mole ratios of 3:5:1, yielding the empirical formula C3H5Cl. Using the given molar mass of 153 g/mol, the molecular formula is determined to be C6H10Cl2.

Step by step solution

01

Calculate the moles of each element

To find the mole ratios, we will assume that we have exactly 100 g of the compound. This means that the given percentages can be directly used as masses. Then, we will convert the mass of each element to moles using their molar masses. - Carbon: \(47.08 g\) C (\(\frac{1 mol}{12.01 g}\)) = \(3.92\) mol C - Hydrogen: \(6.59 g\) H (\(\frac{1 mol}{1.008 g}\)) = \(6.54\) mol H - Chlorine: \(46.33 g\) Cl (\(\frac{1 mol}{35.45 g}\)) = \(1.31\) mol Cl
02

Determine the empirical formula

First, divide each mole value by the smallest mole value to find the mole ratio of each element. - Carbon: \(\frac{3.92}{1.31}\) ≈ \(3\) - Hydrogen: \(\frac{6.54}{1.31}\) ≈ \(5\) - Chlorine: \(\frac{1.31}{1.31}\) = \(1\) The empirical formula is C3H5Cl.
03

Calculate the molar mass of the empirical formula

Now we need to find the molar mass of the empirical formula to determine how many times the empirical formula repeats in the molecular formula. Molar mass of C3H5Cl = (3 × 12.01) + (5 × 1.008) + (1 × 35.45) ≈ \(77.5 g/mol\)
04

Find the molecular formula

We can find the number of times the empirical formula repeats in the molecular formula by dividing the given molar mass by the empirical formula's molar mass and rounding to the nearest whole number: \(\frac{153 g/mol}{77.5 g/mol}\) ≈ \(2\) The molecular formula is thus the empirical formula repeated 2 times: (C3H5Cl)2 = C6H10Cl2. The empirical formula is C3H5Cl, and the molecular formula is C6H10Cl2.

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Most popular questions from this chapter

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