Problem 79 - Chemistry The Science in Context

Question

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

Step-by-Step Solution

Answer

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 1: (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

Step 2: (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%

Key Concepts

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.