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Chapter 3: Problem 48

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{HCO}_{2}\), molar mass \(=90.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\), molar mass \(=88 \mathrm{~g} / \mathrm{mol}\)

Short Answer

Expert verified
The molecular formulas for the given compounds are: (a) \(\mathrm{H_{2}C_{2}O_{4}\) (b) \(\mathrm{C_{4}H_{8}O_{2}\)

Step by step solution

01

Calculate the molar mass of the empirical formulas

For each given empirical formula, calculate its molar mass using the atomic masses of the elements present in the empirical formula. (a) For the empirical formula \(\mathrm{HCO}_{2}\): Molar mass of H: 1 g/mol Molar mass of C: 12 g/mol Molar mass of O: 16 g/mol Molar mass = (1)(1) + (1)(12) + (2)(16) = 1 + 12 + 32 = 45 g/mol (b) For the empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\): Molar mass of C: 12 g/mol Molar mass of H: 1 g/mol Molar mass of O: 16 g/mol Molar mass = (2)(12) + (4)(1) + (1)(16) = 24 + 4 + 16 = 44 g/mol
02

Calculate the ratio between the molar mass of the compound and the empirical formula

For each given compound, divide the molar mass of the compound by the molar mass of its empirical formula. (a) Ratio for \(\mathrm{HCO}_{2}\) compound: \(\frac{90.0 \ \mathrm{g/mol}}{45 \ \mathrm{g/mol}} = 2\) (b) Ratio for \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) compound: \(\frac{88 \ \mathrm{g/mol}}{44 \ \mathrm{g/mol}} = 2\)
03

Multiply the empirical formula by the ratio to find the molecular formula

For each compound, multiply the coefficients of the elements in the empirical formula by the ratio calculated in step 2. (a) Molecular formula for \(\mathrm{HCO}_{2}\) compound: \(\mathrm{(H_{1}C_{1}O_{2})} \times 2 = \mathrm{H_{2}C_{2}O_{4}}\) (b) Molecular formula for \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) compound: \(\mathrm{(C_{2}H_{4}O_{1})} \times 2 = \mathrm{C_{4}H_{8}O_{2}}\) Therefore, the molecular formulas for the given compounds are as follows: (a) \(\mathrm{H_{2}C_{2}O_{4}}\) (b) \(\mathrm{C_{4}H_{8}O_{2}}\)

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Most popular questions from this chapter

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\), \(8.80 \% \mathrm{H}\), and \(15.51 \%\) O by mass, and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H}\), and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\). (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \% \mathrm{C}, 7.1 \% \mathrm{H}, 26.2 \% \mathrm{O}\), and \(7.7 \% \mathrm{~N}\) by mass; its \(\mathrm{MW}\) is about \(180 \mathrm{amu}\).

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(10.4 \% \mathrm{C}, 27.8 \% \mathrm{~S}\), and \(61.7 \% \mathrm{Cl}\) (b) \(21.7 \% \mathrm{C}, 9.6 \% \mathrm{O}\), and \(68.7 \% \mathrm{~F}\) (c) \(32.79 \% \mathrm{Na}, 13.02 \% \mathrm{Al}\), and \(54.19 \% \mathrm{~F}\)

Very small crystals composed of 1000 to 100,000 atoms, called quantum dots, are being investigated for use in electronic devices. (a) A quantum dot was made of solid silicon in the shape of a sphere, with a diameter of \(4 \mathrm{~nm}\). CalcuJate the mass of the quantum dot, using the density of silicon \(\left(23 \mathrm{~g} / \mathrm{cm}^{3}\right)\). (b) How many silicon atoms are in the quantum dot? (c) The density of germanium is \(5.325 \mathrm{~g} / \mathrm{cm}^{3}\). If you made a \(4 \mathrm{~nm}\) quantum dot of germanium, how many Ge atoms would it contain? Assume the dot is spherical

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing number of atoms: \(3.0 \times 10^{23}\) molecules of \(\mathrm{H}_{2} \mathrm{O}_{2}, 2.0 \mathrm{~mol} \mathrm{CH}_{4}, 32 \mathrm{~g} \mathrm{O}_{2}\).

Copper is an excellent electrical conductor widely used in making electric circuits. In producing a printed circuit board for the electronics industry, a layer of copper is laminated on a plastic board. A circuit pattern is then printed on the board using a chemically resistant polymer. The board is then exposed to a chemical bath that reacts with the exposed copper, leaving the desired copper circuit, which has been protected by the overlaying polymer. Finally, a solvent removes the polymer. One reaction used to remove the exposed copper from the circuit board is \(\mathrm{Cu}(\mathrm{s})+\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}(a q)+4 \mathrm{NH}_{3}(a q) \longrightarrow\) \(2 \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}(a q)\) A plant needs to produce 5000 circuit boards, each with a surface area measuring \(2.0\) in. \(\times 3.0\) in. The boards are covered with a \(0.65-\mathrm{mm}\) layer of copper. In subsequent processing, \(85 \%\) of the copper is removed. Copper has a density of \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\) \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) needed to produce the circuit boards, assuming that the reaction used gives a \(97 \%\) yield.
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