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Chapter 3: Problem 47

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{2}\), molar mass \(=84 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)

Short Answer

Expert verified
The molecular formulas for the given compounds are (a) \(\mathrm{C}_{6}\mathrm{H}_{12}\) and (b) \(\mathrm{NH}_{2}\mathrm{Cl}\).

Step by step solution

01

Calculate empirical formula molar mass.

To calculate the empirical formula molar mass, add the molar mass of each element in the empirical formula, so for \(\mathrm{CH}_{2}\), that is C (Carbon - \(12.01 g/mol\)) and H (Hydrogen - \(1.01 g/mol\) each): Empirical formula molar mass = \(12.01 + (2 * 1.01) = 14.03\text{ g/mol}\)
02

Calculate molecular formula multiplier ratio.

Divide the given molar mass of the molecular formula by the molar mass of the empirical formula, and round to the nearest whole number: Ratio = \(\frac{84}{14.03} = 5.99 \approx 6\)
03

Determine the molecular formula.

Multiply the empirical formula by the ratio calculated in step 2, this will give the molecular formula. In this case, \(\mathrm{CH}_{2} \times 6 = \mathrm{C}_{6}\mathrm{H}_{12}\). The molecular formula for compound (a) is \(\mathrm{C}_{6}\mathrm{H}_{12}\). b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)
04

Calculate empirical formula molar mass.

To calculate the empirical formula molar mass, add the molar mass of each element in the empirical formula, so for \(\mathrm{NH}_{2} \mathrm{Cl}\), that is N (Nitrogen - \(14.01 g/mol\)), H (Hydrogen - \(1.01 g/mol\) each), and Cl (Chlorine - \(35.45 g/mol\)): Empirical formula molar mass = \(14.01 + (2 * 1.01) + 35.45 = 51.48\text{ g/mol}\)
05

Calculate molecular formula multiplier ratio.

Divide the given molar mass of the molecular formula by the molar mass of the empirical formula, and round to the nearest whole number: Ratio = \(\frac{51.5}{51.48} = 1.0004 \approx 1\)
06

Determine the molecular formula.

Multiply the empirical formula by the ratio calculated in step 2, this will give the molecular formula. In this case, \(\mathrm{NH}_{2} \mathrm{Cl} \times 1 = \mathrm{NH}_{2}\mathrm{Cl}\). The molecular formula for compound (b) is \(\mathrm{NH}_{2}\mathrm{Cl}\).

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Most popular questions from this chapter

A mixture containing \(\mathrm{KCIO}_{3}, \mathrm{~K}_{2} \mathrm{CO}_{3}, \mathrm{KHCO}_{3}\), and \(\mathrm{KCl}\) was heated, producing \(\mathrm{CO}_{2}, \mathrm{O}_{2}\), and \(\mathrm{H}_{2} \mathrm{O}\) gases according to the following equations: $$ \begin{aligned} 2 \mathrm{KClO}_{3}(\mathrm{~s}) & \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g) \\ 2 \mathrm{KHCO}_{3}(\mathrm{~s}) & \longrightarrow \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{CO}_{2}(g) \\ \mathrm{K}_{2} \mathrm{CO}_{3}(s) & \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{CO}_{2}(g) \end{aligned} $$ The KCl does not react under the conditions of the reaction. If \(100.0 \mathrm{~g}\) of the mixture produces \(1.80 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\), \(13.20 \mathrm{~g}\) of \(\mathrm{CO}_{2}\), and \(4.00 \mathrm{~g}\) of \(\mathrm{O}_{2}\), what was the composition of the original mixture? (Assume complete decomposition of the mixture.)

Glycine, an amino acid used by organisms to make proteins, is represented by the molecular model below. (a) Write its molecular formula. (b) Determine its molar mass. (c) Calculate the mass of 3 moles of glycine. (d) Calculate the percent nitrogen by mass in glycine. [Sections \(3.3\) and \(3.5]\)

Hydrofluoric acid, \(\mathrm{HF}(a q)\), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the \(\mathrm{HF}(a q) .\) Sodium silicate \(\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right)\), for example, reacts as follows: \(\mathrm{Na}_{2} \mathrm{SiO}_{3}(\mathrm{~s})+8 \mathrm{HF}(a q) \longrightarrow\) $$ \mathrm{H}_{2} \mathrm{SiF}_{6}(a q)+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of \(\mathrm{HF}\) are needed to react with \(0.300 \mathrm{~mol}\) of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with \(0.800 \mathrm{~g}\) of HF?

(a) What is the mass, in grams, of \(0.0714 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(8.776 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(6.52 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{\mathrm{g}} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{8}\) ) if \(0.05570\) mol weighs \(15.86 \mathrm{~g}\) ?

Calculate the following quantities: (a) mass, in grams, of \(0.105\) moles sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) (b) moles of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\) in \(14350 \mathrm{~g}\) of this substance (c) number of molecules in \(1.0 \times 10^{-6} \mathrm{~mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (d) number of \(\mathrm{N}\) atoms in \(0.410 \mathrm{~mol} \mathrm{NH}_{3}\)
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