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Chapter 5: Problem 90

Maleic acid is an organic compound composed of \(41.39 \%\) C, \(3.47 \%\) H, and the rest oxygen. If 0.129 mole of maleic acid has a mass of \(15.0 \mathrm{g},\) what are the empirical and molecular formulas of maleic acid?

Short Answer

Expert verified
The empirical formula for maleic acid is \(C_2H_2O_2\), and the molecular formula is \(C_4H_2O_4\).

Step by step solution

01

Calculate moles of each element from their percentages

Divide the percentage composition by the molar mass of each element: \( moles\ of\ Carbon = \frac{41.39\%}{12.01\:g/mol} \) \( moles\ of\ Hydrogen = \frac{3.47\%}{1.01\:g/mol} \) \$ moles\ of\ Oxygen = 100\% - 41.39\% - 3.47\% = 55.14\% \$, then divide by its molar mass: \( moles\ of\ Oxygen = \frac{55.14\%}{16.00\:g/mol} \)
02

Convert percentages to simplest whole number ratios

To find the simplest whole number ratio of moles, divide each amount by the smallest mole value: \(C: \frac{41.39/12.01}{3.47/1.01} = 2 \) \(H: \frac{3.47/1.01}{3.47/1.01} = 1 \) \(O: \frac{55.14/16.00}{3.47/1.01} = 2 \) So the empirical formula is: \(C_2H_2O_2\)
03

Calculate molar mass of empirical formula

Find the molar mass of the empirical formula \(C_2H_2O_2\) by adding together the molar masses of its constituent elements: \( Molar\:mass\:of\:C_2H_2O_2 = 2(12.01\:g/mol) + 2(1.01\:g/mol) + 2(16.00\:g/mol) = 58.04\:g/mol \)
04

Calculate molar mass of the molecular formula

We know the mass of 0.129 moles of maleic acid is 15.0 grams. So the molar mass of the molecular formula is: \(Molar\:mass\:of\:molecular\:formula = \frac{15.0\:g}{0.129\:mol} = 116.28\:g/mol \)
05

Determine molecular formula

Divide the molar mass of the molecular formula by the molar mass of the empirical formula to find the ratio (n) of the molecular formula to the empirical formula: \(n = \frac{116.28\:g/mol}{58.04\:g/mol} = 2 \) Thus, the molecular formula is: \(C_{2(2)}H_{2(1)}O_{2(2)} = C_4H_2O_4\) The empirical formula for maleic acid is \(C_2H_2O_2\), and the molecular formula is \(C_4H_2O_4\).

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Most popular questions from this chapter

A sample of urea contains \(1.121 \mathrm{g} \mathrm{N}, 0.161 \mathrm{g} \mathrm{H}, 0.480 \mathrm{g} \mathrm{C}\) and \(0.640 \mathrm{g}\) O. What is the empirical formula of urea?

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