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Chapter 3: Problem 22

Determine the formula weights of each of the following compounds: (a) nitrous oxide, \(\mathrm{N}_{2} \mathrm{O},\) known as laughing gas and used as an anesthetic in dentistry; (b) benzoic acid, \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\), a substance used as a food preservative; (c) \(\mathrm{Mg}(\mathrm{OH})_{2}\), the active ingredient in milk of magnesia; (d) urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}, \mathrm{a}\) compound used as a nitrogen fertilizer; (e) isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\), responsible for the odor of bananas.

Short Answer

Expert verified
The formula weights of the given compounds are as follows: (a) Nitrous oxide, $\mathrm{N}_{2} \mathrm{O}$: 44.013 g/mol (b) Benzoic acid, $\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}$: 122.123 g/mol (c) Magnesium hydroxide, $\mathrm{Mg}(\mathrm{OH})_{2}$: 58.319 g/mol (d) Urea, $\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}$: 60.056 g/mol (e) Isopentyl acetate, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}$: 114.188 g/mol

Step by step solution

01

(a) Formula weight of Nitrous oxide (N2O)

: 1. Identify elements: Nitrogen (N) and Oxygen (O) 2. Atomic weights: Nitrogen (N) = 14.007, Oxygen (O) = 15.999 3. Multiply by the number of atoms: (2 脳 14.007) + (1 脳 15.999) 4. Formula weight of N2O = 28.014 + 15.999 = 44.013 g/mol
02

(b) Formula weight of Benzoic acid (HC7H5O2)

: 1. Identify elements: Hydrogen (H), Carbon (C), and Oxygen (O) 2. Atomic weights: Hydrogen (H) = 1.008, Carbon (C) = 12.011, Oxygen (O) = 15.999 3. Multiply by the number of atoms: (1 脳 1.008) + (7 脳 12.011) + (5 脳 1.008) + (2 脳 15.999) 4. Formula weight of HC7H5O2 = 1.008 + 84.077 + 5.040 + 31.998 = 122.123 g/mol
03

(c) Formula weight of Mg(OH)2

: 1. Identify elements: Magnesium (Mg), Oxygen (O), and Hydrogen (H) 2. Atomic weights: Magnesium (Mg) = 24.305, Oxygen (O) = 15.999, Hydrogen (H) = 1.008 3. Multiply by the number of atoms: (1 脳 24.305) + (2 脳 15.999) + (2 脳 1.008) 4. Formula weight of Mg(OH)2 = 24.305 + 31.998 + 2.016 = 58.319 g/mol
04

(d) Formula weight of Urea ((NH2)2CO)

: 1. Identify elements: Nitrogen (N), Hydrogen (H), Carbon (C), and Oxygen (O) 2. Atomic weights: Nitrogen (N) = 14.007, Hydrogen (H) = 1.008, Carbon (C) = 12.011, Oxygen (O) = 15.999 3. Multiply by the number of atoms: (2 脳 14.007) + (4 脳 1.008) + (1 脳 12.011) + (1 脳 15.999) 4. Formula weight of (NH2)2CO = 28.014 + 4.032 + 12.011 + 15.999 = 60.056 g/mol
05

(e) Formula weight of Isopentyl acetate (CH3CO2C5H11)

: 1. Identify elements: Hydrogen (H), Carbon (C), and Oxygen (O) 2. Atomic weights: Hydrogen (H) = 1.008, Carbon (C) = 12.011, Oxygen (O) = 15.999 3. Multiply by the number of atoms: (3 脳 1.008) + (2 脳 12.011) + (5 脳 12.011) + (11 脳 1.008) + (1 脳 15.999) 4. Formula weight of CH3CO2C5H11 = 3.024 + 24.022 + 60.055 + 11.088 + 15.999 = 114.188 g/mol

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Weight
Every element has a unique atomic weight, which is essentially the average mass of atoms of an element, calculated using the relative abundance of isotopes. This concept helps us to compute more complex measurements like formula or molecular weights. In simple terms:
  • The atomic weight is measured in atomic mass units (amu), where 1 amu is defined as a twelfth of the mass of an atom of carbon-12.
  • Each element's atomic weight is slightly different due to isotopic variations, meaning some naturally occurring atoms have extra neutrons.
When looking at nitrous oxide, for example, we use the atomic weights of nitrogen (14.007 amu) and oxygen (15.999 amu) to calculate its formula weight.
Chemical Compounds
Chemical compounds are substances formed from two or more elements that are chemically bonded in a fixed ratio. The properties of these compounds are distinct from their elements. Understanding chemical compounds involves examining:
  • The types of bonds (ionic, covalent) holding the atoms together.
  • The ratio of each element present in the compound.
  • Specific examples, like nitrous oxide ( _2O), benzoic acid ( HC_7H_5O_2), and others, which demonstrate fixed proportions and unique properties.
Chemical compounds make up all the materials around us, including synthetic and natural substances. This concept is a stepping stone to more complex topics in chemistry.
Molecular Formula
A molecular formula provides the exact number of different atoms in a single molecule of a compound. This is different from an empirical formula, which shows the simplest whole-number ratio of atoms in the compound. Here are key aspects of molecular formulas:
  • They are used for defining the composition of a molecule, showing each type of atom and its quantity.
  • Compounds like benzoic acid have molecular formulas that not only represent the elements present but their exact numbers, like C_7H_5O_2.
  • Molecular formulas are critical for determining the molecular weights necessary in chemical calculations.
Understanding these formulas is crucial for problem-solving in chemistry, revealing the detailed makeup of a compound.
Problem Solving in Chemistry
Approaching problems in chemistry, such as calculating formula weights, involves a systematic method. This method breaks down complex chemical questions into manageable steps:
  • Start by identifying the elements present in the chemical formula and note their atomic weights.
  • Multiply each atom's atomic weight by the number of times it appears in the formula.
  • Sum these values to find the formula weight and express it in grams per mole.
For example, computing the formula weight of urea involves taking into account the correct amount of nitrogen, hydrogen, carbon, and oxygen in its molecular formula, (NH_2)_2CO. Problem-solving skills in chemistry are honed by practicing these calculations, understanding the principles backing them, and being attentive to detail. These steps are crucial for accuracy in both academic and practical chemistry applications.

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Most popular questions from this chapter

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 \(4 \mathrm{nm} .\) Calculate the mass of the quantum dot, using the density of silicon \(\left(2.3 \mathrm{~g} / \mathrm{cm}^{3}\right)\) (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-nm quantum dot of germanium, how many Ge atoms would it contain? Assume the dot is spherical.

(a) Define the terms limiting reactant and excess reactant. (b) Why are the amounts of products formed in a reaction determined only by the amount of the limiting reactant? (c) Why should you base your choice of which compound is the limiting reactant on its number of initial moles, not on its initial mass in grams?

One of the steps in the commercial process for converting ammonia to nitric acid is the conversion of \(\mathrm{NH}_{3}\) to NO: \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) In a certain experiment, \(2.00 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) reacts with \(2.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) (a) Which is the limiting reactant? (b) How many grams of \(\mathrm{NO}\) and of \(\mathrm{H}_{2} \mathrm{O}\) form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed? (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Detonation of nitroglycerin proceeds as follows: $$ 4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}_{3} \mathrm{O}_{9}(l) \longrightarrow \\ \quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad12 \mathrm{CO}_{2}(g)+6 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) If a sample containing 2.00 \(\mathrm{mL}\) of nitroglycerin (density \(=\) 1.592 \(\mathrm{g} / \mathrm{mL}\) ) is detonated, how many moles of gas are produced? (b) If each mole of gas occupies 55 Lunder the conditions of the explosion, how many liters of gas are produced? (c) How many grams of \(\mathrm{N}_{2}\) are produced in the detonation?

Write balanced chemical equations to correspond to each of the following descriptions: (a) Solid calcium carbide, \(\mathrm{CaC}_{2}\), reacts with water to form an aqueous solution of calcium hydroxide and acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\). (b) When solid potassium chlorate is heated, it decomposes to form solid potassium chloride and oxygen gas. (c) Solid zinc metal reacts with sulfuric acid to form hydrogen gas and an aqueous solution of zinc sulfate. (d) When liquid phosphorus trichloride is added to water, it reacts to form aqueous phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}(a q),\) and aqueous hydrochloric acid. (e) When hydrogen sulfide gas is passed over solid hot iron(III) hydroxide, the resultant reaction produces solid iron(III) sulfide and gaseous water.
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