Problem 47 - Chemistry: An Atoms-Focused Approach

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 the following compounds: (a) Na2O, (b) NaOH, (c) NaHCO3, and (d) Na2CO3. Answer: (a) Na2O: 74.21% Na and 25.79% O (b) NaOH: 57.48% Na, 40.00% O, and 2.53% H (c) NaHCO3: 27.38% Na, 1.20% H, 14.30% C, and 57.13% O (d) Na2CO3: 43.38% Na, 11.33% C, and 45.29% O

Step 1: (a) Percent composition of Na2O

First, let's find the molar mass of Na2O: 2 * molar mass of Na + molar mass of O = 2 * 22.99 g/mol + 16.00 g/mol = 45.98 g/mol + 16.00 g/mol = 61.98 g/mol Now, calculate the percent composition of each element: Percent of Na = (mass of Na / molar mass of Na2O) * 100 = (45.98 g / 61.98 g) * 100 = 74.21 % Percent of O = (mass of O / molar mass of Na2O) * 100 = (16.00 g / 61.98 g) * 100 = 25.79 % Therefore, the percent composition of Na2O is 74.21% Na and 25.79% O.

Step 2: (b) Percent composition of NaOH

Next, let's find the molar mass of NaOH: molar mass of Na + molar mass of O + molar mass of H = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol Now, calculate the percent composition of each element: Percent of Na = (mass of Na / molar mass of NaOH) * 100 = (22.99 g / 40.00 g) * 100 = 57.48 % Percent of O = (mass of O / molar mass of NaOH) * 100 = (16.00 g / 40.00 g) * 100 = 40.00 % Percent of H = (mass of H / molar mass of NaOH) * 100 = (1.01 g / 40.00 g) * 100 = 2.53 % Therefore, the percent composition of NaOH is 57.48% Na, 40.00% O, and 2.53% H.

Step 3: (c) Percent composition of NaHCO3

Now, let's find the molar mass of NaHCO3: molar mass of Na + molar mass of H + molar mass of C + (3 * molar mass of O) = 22.99 g/mol + 1.01 g/mol + 12.01 g/mol + (3 * 16.00 g/mol) = 84.01 g/mol Now, calculate the percent composition of each element: Percent of Na = (mass of Na / molar mass of NaHCO3) * 100 = (22.99 g / 84.01 g) * 100 = 27.38 % Percent of H = (mass of H / molar mass of NaHCO3) * 100 = (1.01 g / 84.01 g) * 100 = 1.20 % Percent of C = (mass of C / molar mass of NaHCO3) * 100 = (12.01 g / 84.01 g) * 100 = 14.30 % Percent of O = (mass of O / molar mass of NaHCO3) * 100 = (48.00 g / 84.01 g) * 100 = 57.13 % Therefore, the percent composition of NaHCO3 is 27.38% Na, 1.20% H, 14.30% C, and 57.13% O.

Step 4: (d) Percent composition of Na2CO3

Finally, let's find the molar mass of Na2CO3: (2 * molar mass of Na) + molar mass of C + (3 * molar mass of O) = (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol) = 105.98 g/mol Now, calculate the percent composition of each element: Percent of Na = (mass of Na / molar mass of Na2CO3) * 100 = (45.98 g / 105.98 g) * 100 = 43.38 % Percent of C = (mass of C / molar mass of Na2CO3) * 100 = (12.01 g / 105.98 g) * 100 = 11.33 % Percent of O = (mass of O / molar mass of Na2CO3) * 100 = (48.00 g / 105.98 g) * 100 = 45.29 % Therefore, the percent composition of Na2CO3 is 43.38% Na, 11.33% C, and 45.29% O.

Key Concepts

Molar Mass

The molar mass of a compound is a crucial concept when calculating percent composition. It represents the weight of one mole of a substance, expressed in grams per mole (g/mol). To determine the molar mass, you need to add up the atomic masses of all the atoms present in the compound's chemical formula.
For example, in the compound \(\text{Na}_2\text{O}\), the molar mass is calculated by adding the masses of sodium and oxygen. With sodium having an atomic mass of 22.99 g/mol and oxygen 16.00 g/mol, the molar mass calculation is straightforward:
\[2 \times 22.99 \, \text{g/mol} + 16.00 \, \text{g/mol} = 61.98 \, \text{g/mol}\]
This molar mass is pivotal for understanding the amount of each element in the compound, guiding you towards the correct percent composition.

Chemical Formula

The chemical formula of a compound is like a recipe. It tells us what elements are present and in what quantities. It's a shorthand way of depicting the elements that make up a compound using their symbols and numerical subscripts.
A chemical formula not only helps in naming the compound but also in computing the molar mass and percent composition. For instance, the formula \(\text{Na}_2\text{O}\) tells us that there are two sodium atoms for every one oxygen atom. The subscript numbers are key here as they indicate the ratio of atoms, guiding us in calculating the correct molar mass:

• Sodium (\(\text{Na}\)): two atoms
• Oxygen (\(\text{O}\)): one atom

This accurate depiction ensures precision in further mathematical computations like determining the molar mass and, subsequently, percent composition.

Stoichiometry

Stoichiometry is the bridge between the chemical equation and the real-world quantities we measure and use. It involves calculations based on the relationships between the amounts of reactants and products in chemical reactions.
In the context of percent composition, stoichiometry helps us understand how much of each element is present in a compound. By knowing the molar masses and using stoichiometry, you can convert between grams and moles of a substance. This is crucial for finding the percent of each component within a compound formula.
When you determine percent composition, stoichiometry allows you to comprehend how each element contributes to the total mass of the compound. For instance, in \(\text{NaOH}\), stoichiometry helps you calculate that sodium makes up 57.48% of the mass, oxygen 40.00%, and hydrogen 2.53%. These calculations are bolstered by stoichiometric principles, ensuring precision and accuracy.