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Chapter 3: Problem 82

Determine the molecular formulas to which the following empirical formulas and molar masses pertain. a. \(\mathrm{SNH}(188.35 \mathrm{~g} / \mathrm{mol})\) b. \(\mathrm{NPCl}_{2}(347.64 \mathrm{~g} / \mathrm{mol})\) c. \(\mathrm{CoC}_{4} \mathrm{O}_{4}(341.94 \mathrm{~g} / \mathrm{mol})\) d. \(\mathrm{SN}(184.32 \mathrm{~g} / \mathrm{mol})\)

Short Answer

Expert verified
The molecular formulas for the given empirical formulas and molar masses are: a. \(\mathrm{(SNH)_{4}}\) b. \(\mathrm{(NPCl_{2})_{3}}\) c. \(\mathrm{(CoC}_{4} \mathrm{O}_{4})_{2}\) d. \(\mathrm{(SN)_{4}}\)

Step by step solution

01

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{SNH}\). S: 32.07 g/mol N: 14.01 g/mol H: 1.01 g/mol Molar mass of \(\mathrm{SNH}\) = (32.07 + 14.01 + 1.01) g/mol = 47.09 g/mol.
02

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (188.35 g/mol) / (47.09 g/mol) ≈ 4
03

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(SNH)_{4}}\) b. \(\mathrm{NPCl}_{2}(347.64 \mathrm{~g/mol})\)
04

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{NPCl}_{2}\). N: 14.01 g/mol P: 30.97 g/mol Cl: 35.45 g/mol Molar mass of \(\mathrm{NPCl}_{2}\) = (14.01 + 30.97 + 35.45*2) g/mol = 116.33 g/mol.
05

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (347.64 g/mol) / (116.33 g/mol) ≈ 3
06

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(NPCl_{2})_{3}}\) c. \(\mathrm{CoC}_{4}\mathrm{O}_{4}(341.94 \mathrm{~g/mol})\)
07

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{CoC}_{4} \mathrm{O}_{4}\). Co: 58.93 g/mol C: 12.01 g/mol O: 16.00 g/mol Molar mass of \(\mathrm{CoC}_{4} \mathrm{O}_{4}\) = (58.93 + 12.01*4 + 16.00*4) g/mol = 170.97 g/mol.
08

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (341.94 g/mol) / (170.97 g/mol) ≈ 2
09

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(CoC}_{4} \mathrm{O}_{4})_{2}\) d. \(\mathrm{SN}(184.32 \mathrm{~g/mol})\)
10

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{SN}\). S: 32.07 g/mol N: 14.01 g/mol Molar mass of \(\mathrm{SN}\) = (32.07 + 14.01) g/mol = 46.08 g/mol.
11

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (184.32 g/mol) / (46.08 g/mol) ≈ 4
12

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(SN)_{4}}\)

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Most popular questions from this chapter

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O} $$ \(\begin{array}{lll}\text { chlorobenzene } & \text { chloral } & \text { DDT }\end{array}\) In a government lab, \(1142 \mathrm{~g}\) of chlorobenzene is reacted with \(485 \mathrm{~g}\) of chloral. a. What mass of DDT is formed, assuming \(100 \%\) yield? b. Which reactant is limiting? Which is in excess? c. What mass of the excess reactant is left over? d. If the actual yield of DDT is \(200.0 \mathrm{~g}\), what is the percent yield?

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, \(\mathrm{H}\), and \(\mathrm{O}\). Combustion of \(19.81 \mathrm{mg}\) terephthalic acid produces \(41.98 \mathrm{mg} \mathrm{CO}_{2}\) and \(6.45 \mathrm{mg} \mathrm{H}_{2} \mathrm{O}\). If \(0.250 \mathrm{~mole}\) of terephthalic acid has a mass of \(41.5 \mathrm{~g}\), determine the molecular formula for terephthalic acid.

Acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}\right)\) is the starting material for many synthetic carpets and fabrics. It is produced by the following reaction. \(2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) If \(15.0 \mathrm{~g} \mathrm{C}_{3} \mathrm{H}_{6}, 10.0 \mathrm{~g} \mathrm{O}_{2}\), and \(5.00 \mathrm{~g} \mathrm{NH}_{3}\) are reacted, what mass of acrylonitrile can be produced, assuming \(100 \%\) yield?

Give the balanced equation for each of the following chemical reactions: a. Glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) reacts with oxygen gas to produce gaseous carbon dioxide and water vapor. b. Solid iron(III) sulfide reacts with gaseous hydrogen chloride to form solid iron(III) chloride and hydrogen sulfide gas. c. Carbon disulfide liquid reacts with ammonia gas to produce hydrogen sulfide gas and solid ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\).

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: \(3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow\) $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2}\) \(\mathrm{mg} \mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(\mathrm{~g})\) could be produced from such a mixture?
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