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Chapter 3: Problem 79

Calculate the percent composition of (a) \(\mathrm{Na}_{2} \mathrm{O},\) (b) \(\mathrm{NaOH}\) (c) \(\mathrm{NaHCO}_{3},\) and \((\mathrm{d}) \mathrm{Na}_{2} \mathrm{CO}_{3}\).

Short Answer

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Question: Calculate the percent composition of each element in the following compounds: (a) Na2O, (b) NaOH, (c) NaHCO3, and (d) Na2CO3. Answer: (a) Na2O: Percent composition of Na = 74.20% Percent composition of O = 25.80% (b) NaOH: Percent composition of Na = 57.48% Percent composition of O = 40.00% Percent composition of H = 2.52% (c) NaHCO3: Percent composition of Na = 27.37% Percent composition of H = 1.20% Percent composition of C = 14.30% Percent composition of O = 57.13% (d) Na2CO3: Percent composition of Na = 43.38% Percent composition of C = 11.32% Percent composition of O = 45.30%

Step by step solution

01

(Step 1: Determine the molar mass of each compound)

(To find the molar mass of compounds, you can use the periodic table to find the atomic mass of each element in the compound and add them together. The molar mass of a compound is the sum of the atomic masses of the elements in the compound. Remember that the molar mass of a compound is usually given in grams per mole (g/mol).) (a) Na2O Molar mass of Na2O = (2 * Atomic mass of Na) + Atomic mass of O = (2 * 22.99 g/mol) + 16 g/mol = 45.98 g/mol + 16 g/mol = 61.98 g/mol (b) NaOH Molar mass of NaOH = Atomic mass of Na + Atomic mass of O + Atomic mass of H = 22.99 g/mol + 16 g/mol + 1.01 g/mol = 40 g/mol (c) NaHCO3 Molar mass of NaHCO3 = Atomic mass of Na + Atomic mass of H + Atomic mass of C + (3* Atomic mass of O) = 22.99 g/mol + 1.01 g/mol + 12.01 g/mol + (3 * 16 g/mol) = 84.01 g/mol (d) Na2CO3 Molar mass of Na2CO3 = (2 * Atomic mass of Na) + Atomic mass of C + (3 * Atomic mass of O) = (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16 g/mol) = 105.99 g/mol
02

(Step 2: Calculate the percent composition)

(To find the percent composition of each element in the compound, divide the molar mass of the individual element by the molar mass of the compound and multiply by 100.) (a) Na2O: Percent composition of Na = ((2 * Atomic mass of Na) / Molar mass of Na2O) * 100 = (45.98 g/mol / 61.98 g/mol) * 100 = 74.20% Percent composition of O = (Atomic mass of O / Molar mass of Na2O) * 100 = (16 g/mol / 61.98 g/mol) * 100 = 25.80% (b) NaOH: Percent composition of Na = (Atomic mass of Na / Molar mass of NaOH) * 100 = (22.99 g/mol / 40 g/mol) * 100 = 57.48% Percent composition of O = (Atomic mass of O / Molar mass of NaOH) * 100 = (16 g/mol / 40 g/mol) * 100 = 40.00% Percent composition of H = (Atomic mass of H / Molar mass of NaOH) * 100 = (1.01 g/mol / 40 g/mol) * 100 = 2.52% (c) NaHCO3: Percent composition of Na = (Atomic mass of Na / Molar mass of NaHCO3) * 100 = (22.99 g/mol / 84.01 g/mol) * 100 = 27.37% Percent composition of H = (Atomic mass of H / Molar mass of NaHCO3) * 100 = (1.01 g/mol / 84.01 g/mol) * 100 = 1.20% Percent composition of C = (Atomic mass of C / Molar mass of NaHCO3) * 100 = (12.01 g/mol / 84.01 g/mol) * 100 = 14.30% Percent composition of O = (3 * Atomic mass of O / Molar mass of NaHCO3) * 100 = (48 g/mol / 84.01 g/mol) * 100 = 57.13% (d) Na2CO3: Percent composition of Na = (2 * Atomic mass of Na / Molar mass of Na2CO3) * 100 = (45.98 g/mol / 105.99 g/mol) * 100 = 43.38% Percent composition of C = (Atomic mass of C / Molar mass of Na2CO3) * 100 = (12.01 g/mol / 105.99 g/mol) * 100 = 11.32% Percent composition of O = (3 * Atomic mass of O / Molar mass of Na2CO3) * 100 = (48 g/mol / 105.99 g/mol) * 100 = 45.30%

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Key Concepts

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

Molar Mass Calculation
To uncover the molar mass of a chemical compound, start by using the periodic table to find the atomic masses of each element involved. For example, when figuring out the molar mass of sodium oxide, Na extsubscript{2}O, we observe it comprises two sodium atoms and one oxygen atom.
  • The atomic mass of sodium (Na) is 22.99 g/mol.
  • Since there are two Na atoms, we multiply it by 2, yielding 45.98 g/mol.
  • Oxygen (O) has an atomic mass of 16 g/mol.
  • Add them up to get the total molar mass: 45.98 g/mol + 16 g/mol = 61.98 g/mol.
It's really just about putting the pieces of a puzzle together, counting how many of each atom you have and combining their atomic masses.
Chemical Compounds
Chemical compounds are substances comprised of two or more different types of elements that are chemically bonded together. Think of them as recipes in a cookbook, where each element is an ingredient with a specific role. Each compound, like the ones in our problem such as NaOH, NaHCO extsubscript{3}, and Na extsubscript{2}CO extsubscript{3}, has its own unique structure and combination of elements.
  • NaOH is made of sodium (Na), oxygen (O), and hydrogen (H).
  • NaHCO extsubscript{3} includes sodium (Na), hydrogen (H), carbon (C), and three oxygen atoms (O extsubscript{3}).
  • Lastly, Na extsubscript{2}CO extsubscript{3} contains two sodium atoms, one carbon atom, and three oxygen atoms.
The specific ratios and bonds between these atoms are what give each compound its distinct properties.
Elemental Analysis
Elemental analysis in chemistry refers to examining a substance to determine its composition, often in terms of percentages. In our task, we used it to find the percent composition of elements in compounds. This analysis lets us know how much of each element is present within a compound and is very handy when determining proportions needed in reactions or verifying compound purity.
  • Start by calculating how much each element contributes to the molar mass.
  • Divide the element's total mass by the compound's molar mass and multiply by 100 to get the percentage.
For example, in Na extsubscript{2}O, the calculation showed that sodium accounts for approximately 74.20% of the mass, while oxygen makes up the remaining 25.80%. Such breakdowns illustrate how each atom contributes to the whole, reflecting the interconnectedness of elements within a compound.

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Most popular questions from this chapter

Rebreathing Devices In the first episode of George Lucas's Star Wars series, Qui-Gon Jinn and Obi-Wan Kenobi can visit the underwater world of the Gungans only by using A99 Aquata Breathers, which allow them to survive underwater for up to two hours. While the tiny devices may be from the farfetched world of science fiction, current technology exists for transforming carbon dioxide to oxygen. These self- contained rebreathers are used by a select group of underwater cave explorers and can act as self-rescue devices. The chemistry is based on the following chemical reactions, using either potassium superoxide or sodium peroxide:$$\begin{array}{l}4 \mathrm{KO}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{K}_{2}\mathrm{CO}_{3}(s)+3 \mathrm{O}_{2}(g) \\\2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{O}_{2}(g)\end{array}$$.a. The respiratory rate at rest for an average, healthy adult is 12 breaths per minute. If the average breath takes in \(0.500 \mathrm{L}\) of \(\mathrm{O}_{2}(d=1.429 \mathrm{g} / \mathrm{L})\) into the lungs, how many grams of \(\mathrm{KO}_{2}\) are needed to produce enough oxygen for two hours underwater? b. Would you need more or less \(\mathrm{Na}_{2} \mathrm{O}_{2}\) to produce an equivalent amount of oxygen? c. Given the densities of \(\mathrm{KO}_{2}(2.14 \mathrm{g} / \mathrm{mL})\) and \(\mathrm{Na}_{2} \mathrm{O}_{2}\) \((2.805 \mathrm{g} / \mathrm{mL}),\) which solid material would occupy less volume in a rebreather device?

Some catalytic converters in automobiles contain the manganese oxides \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}\)a. Give the names of \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}\). b. Calculate the percent manganese by mass in \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}\).c. Explain how \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) and \(\mathrm{MnO}_{2}\) are consistent with the law of multiple proportions.

Chromium metal can be produced from the high-temperature reaction of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) [chromium(III) oxide] with silicon or aluminum by each of the following reactions:$$\begin{aligned} \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(\ell) & \rightarrow 2 \mathrm{Cr}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) \\\2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{Si}(\ell) & \rightarrow 4 \mathrm{Cr}(\ell)+3 \mathrm{SiO}_{2}(s)\end{aligned}$$.a. Calculate the number of grams of aluminum required to prepare \(400.0 \mathrm{g}\) of chromium metal by the first reaction. b. Calculate the number of grams of silicon required to prepare \(400.0 \mathrm{g}\) of chromium metal by the second reaction.

If a reaction vessel contains equal masses of Fe and \(\mathrm{S}\), a mass of FeS corresponding to which of the following could theoretically be produced? a. the sum of the masses of \(\mathrm{Fe}\) and \(\mathrm{S}\). b. more than the sum of the masses of Fe and \(S\). c. less than the sum of the masses of Fe and \(S\)..

Composition of Over-the-Counter Medicines Calculate the number of molecules or formula units of compound in each of the following common, over-the-counter medications: a. ibuprofen, a pain reliever and fever reducer that contains \(200.0 \mathrm{mg}\) of the active ingredient, \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\) b. an antacid containing 500.0 mg of calcium carbonate c. an allergy tablet containing 4 mg of chlorpheniramine $$\left(\mathrm{C}_{16} \mathrm{H}_{19} \mathrm{ClN}_{2}\right)$$.
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