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Chapter 3: Problem 51

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 of the two compounds are: (a) \(\mathrm{C}_{6}\mathrm{H}_{12}\) (b) \(\mathrm{NH}_{2}\mathrm{Cl}\)

Step by step solution

01

Calculate the molar mass of the empirical formula

We will find the molar mass of the empirical formula \(\mathrm{CH}_{2}\): C: 1 atom 脳 12.01 g/mol = 12.01 g/mol H: 2 atoms 脳 1.01 g/mol = 2.02 g/mol ----------------------------------------- Total: 14.03 g/mol The molar mass of \(\mathrm{CH}_{2}\) is 14.03 g/mol.
02

Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (84 g/mol) by the molar mass of the empirical formula (14.03 g/mol): Multiple = \(\frac{84}{14.03}\) 鈮� 6
03

Determine the molecular formula

Now, multiply the empirical formula by the multiple: \(\mathrm{CH}_{2}\) 脳 6 = \(\mathrm{C}_{6}\mathrm{H}_{12}\) The molecular formula of the compound 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 the molar mass of the empirical formula

We will find the molar mass of the empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\): N: 1 atom 脳 14.01 g/mol = 14.01 g/mol H: 2 atoms 脳 1.01 g/mol = 2.02 g/mol Cl: 1 atom 脳 35.45 g/mol = 35.45 g/mol ----------------------------------------- Total: 51.48 g/mol The molar mass of \(\mathrm{NH}_{2} \mathrm{Cl}\) is 51.48 g/mol.
05

Calculate the multiple

To find the multiple, we will divide the molar mass of the molecular formula (51.5 g/mol) by the molar mass of the empirical formula (51.48 g/mol): Multiple = \(\frac{51.5}{51.48}\) 鈮� 1
06

Determine the molecular formula

Now, multiply the empirical formula by the multiple: \(\mathrm{NH}_{2} \mathrm{Cl}\) 脳 1 = \(\mathrm{NH}_{2}\mathrm{Cl}\) The molecular formula of the compound is \(\mathrm{NH}_{2}\mathrm{Cl}\).

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Most popular questions from this chapter

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s)\), reacts violently with water to form dissolved boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3}\), and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

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The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), a component of gasoline, proceeds as follows: $$ 2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) How many moles of \(\mathrm{O}_{2}\) are needed to burn \(1.50 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ? (b) How many grams of \(\mathrm{O}_{2}\) are needed to burn \(10.0 \mathrm{~g}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ? (c) Octane has a density of \(0.692 \mathrm{~g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). How many grams of \(\mathrm{O}_{2}\) are required to burn \(15.0 \mathrm{gal}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) (the capacity of an average fuel tank)? (d) How many grams of \(\mathrm{CO}_{2}\) are produced when \(15.0 \mathrm{gal}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) are combusted?
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