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Chapter 3: Problem 37

Indigo, the dye for blue jeans, has a percent composition, by mass, of \(73.27 \%\) C \(, 3.84 \%\) H, \(10.68 \%\) N, and the remainder is oxygen. The molecular mass of indigo is 262.3 u. What is the molecular formula of indigo?

Short Answer

Expert verified
The molecular formula of indigo is \(C_{16}H_{10}N_{2}O_{2}\)

Step by step solution

01

Calculate the Empirical Formula

To calculate the empirical formula, convert the percentage of each element to grams. Assume an initial sample size of 100g, so the percentage of each element corresponds to its mass in gram. In doing so, we get 73.27g of C, 3.84g of H, and 10.68g of N. The amount of Oxygen (O) can be obtained by subtracting the combined masses of C, H and N from the total 100g which gives 12.21g.
02

Convert the Mass to Molecules

Then, convert the mass of each element to moles using their atomic masses. Atomic masses are approximately 12.01g/mol for C, 1.008g/mol for H, 14.007g/mol for N, and 16.00g/mol for O. This yields approximately 6.1 moles of C, 3.8 moles of H, 0.76 moles of N, and 0.76 moles of O.
03

Determine the Ratios

Next, find the ratios of the number of atoms by dividing each value of moles with the smallest number of moles which is 0.76. We will get approximately 8 moles of C, 5 moles of H, 1 mole of N, and 1 mole of O.
04

Obtain the Empirical Formula

Thus, the empirical formula of indigo is \(C_8H_5NO\)
05

Calculate the Empirical Formula Mass

Calculate the empirical formula mass using molar masses. The empirical formula mass of \(C_8H_5NO\) is 132.14 u.
06

Determine the Molecular Formula

Divide the given molecular mass (262.3 u) by the empirical formula mass (132.14 u) to obtain the ratio, which is approximately 2. Therefore, the molecular formula will be the empirical formula multiplied by this ratio. The molecular formula of indigo is \(C_{16}H_{10}N_{2}O_{2}\)

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Most popular questions from this chapter

A sample of the compound MSO \(_{4}\) weighing \(0.1131 \mathrm{g}\) reacts with barium chloride and yields \(0.2193 \mathrm{g} \mathrm{BaSO}_{4}\) What must be the atomic mass of the metal M? [Hint: All the \(\mathrm{SO}_{4}^{2-}\) from the MSO \(_{4}\) appears in the \(\mathrm{BaSO}_{4}\) ]

An oxoacid with the formula \(\mathrm{H}_{x} \mathrm{E}_{y} \mathrm{O}_{z}\) has a formula mass of 178 u, has 13 atoms in its formula unit, contains \(34.80 \%\) by mass, and \(15.38 \%\) by number of atoms, of the element E. What is the element \(\mathrm{E}\), and what is the formula of this oxoacid?

The mineral spodumene has the empirical formula \(\mathrm{LiAlSi}_{2} \mathrm{O}_{6} .\) Given that the percentage of lithium- 6 atoms in naturally occuring lithium is \(7.40 \%,\) how many lithium- 6 atoms are present in a 518 g sample of spodumene?

An isomer of the compound \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHOHCH}_{3}\) is (a) \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{CHOHCH}_{2} \mathrm{CH}_{3}\) (c) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{OH} ;\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{2} \mathrm{CH}_{3}\)

Without doing detailed calculations, explain which of the following has the greatest mass percent of sulfur. $\mathrm{SO}_{2}, \mathrm{S}_{2} \mathrm{Cl}_{2}, \mathrm{Na}_{2} \mathrm{S}, \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}, \mathrm{or} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{SH}$
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