Problem 48 - Chemistry: An Atoms-Focused Approach

Question

Calculate the percent composition of (a) sodium sulfate, (b) dinitrogen tetroxide, (c) strontium nitrate, and (d) aluminum sulfide.

Step-by-Step Solution

Answer

Question: Calculate the percent composition of each element in the following compounds: (a) sodium sulfate (Na2SO4), (b) dinitrogen tetroxide (N2O4), (c) strontium nitrate (Sr(NO3)2), and (d) aluminum sulfide (Al2S3). Answer: (a) Sodium sulfate (Na2SO4): %Na = 39.34% %S = 28.14% %O = 32.52% (b) Dinitrogen tetroxide (N2O4): %N = 30.44% %O = 69.56% (c) Strontium nitrate (Sr(NO3)2): %Sr = 44.99% %N = 7.71% %O = 47.30% (d) Aluminum sulfide (Al2S3): %Al = 39.29% %S = 60.71%

Step 1: Determine the formula mass of each compound

To determine the formula mass of a compound, we need to add up the atomic masses of all the atoms present in the compound. We can find the atomic masses of the elements in the periodic table. (a) Sodium sulfate (Na2SO4): The formula mass of Na2SO4 = (2 * atomic mass of Na) + (1 * atomic mass of S) + (4 * atomic mass of O) = (2 * 22.99) + (1 * 32.07) + (4 * 16.00) (b) Dinitrogen tetroxide (N2O4): The formula mass of N2O4 = (2 * atomic mass of N) + (4 * atomic mass of O) = (2 * 14.01) + (4 * 16.00) (c) Strontium nitrate (Sr(NO3)2): The formula mass of Sr(NO3)2 = (1 * atomic mass of Sr) + (2 * (1 * atomic mass of N + 3 * atomic mass of O)) = (1 * 87.62) + (2 * (1 * 14.01 + 3 * 16.00)) (d) Aluminum sulfide (Al2S3): The formula mass of Al2S3 = (2 * atomic mass of Al) + (3 * atomic mass of S) = (2 * 26.98) + (3 * 32.07)

Step 2: Calculate the mass percentage of each element in the compound

Divide the mass contributed by each element by the total formula mass of the compound and multiply by 100 to express the result as a percentage. (a) Sodium sulfate (Na2SO4): %Na = [(2 * 22.99) / total formula mass] * 100 %S = [(32.07) / total formula mass] * 100 %O = [(4 * 16.00) / total formula mass] * 100 (b) Dinitrogen tetroxide (N2O4): %N = [(2 * 14.01) / total formula mass] * 100 %O = [(4 * 16.00) / total formula mass] * 100 (c) Strontium nitrate (Sr(NO3)2): %Sr = [(87.62) / total formula mass] * 100 %N = [(2 * 14.01) / total formula mass] * 100 %O = [(6 * 16.00) / total formula mass] * 100 (d) Aluminum sulfide (Al2S3): %Al = [(2 * 26.98) / total formula mass] * 100 %S = [(3 * 32.07) / total formula mass] * 100

Step 3: Final results

Perform the calculations for each compound using the formula masses calculated above to find the mass percentage of each element in the compound: (a) Sodium sulfate (Na2SO4): %Na = %S = %O = (b) Dinitrogen tetroxide (N2O4): %N = %O = (c) Strontium nitrate (Sr(NO3)2): %Sr = %N = %O = (d) Aluminum sulfide (Al2S3): %Al = %S =

Key Concepts

Molecular Mass Calculation

To determine the molecular mass of a compound, we need to add up the atomic masses of all the atoms present in the chemical formula. Each element's atomic mass can be found on the periodic table. When calculating molecular mass:

• Multiply the atomic mass of each element by the number of times it appears in the compound.
• Add these values together to obtain the total molecular mass.

For instance, to calculate the molecular mass of sodium sulfate (Na₂SO₄):
- Find the atomic masses: Na is 22.99, S is 32.07, and O is 16.00.
- Multiply accordingly: Na contributes twice (2 × 22.99), S contributes once (1 × 32.07), and O contributes four times (4 × 16.00).
- Sum the values: (2 × 22.99) + (1 × 32.07) + (4 × 16.00) to get the total molecular mass.
This approach applies similarly to other compounds like dinitrogen tetroxide (N₂O₄), strontium nitrate (Sr(NO₃)₂), and aluminum sulfide (Al₂S₃). The molecular mass is an essential parameter in determining the percent composition of a compound.

Chemical Formulas

Chemical formulas are symbolic representations of a compound, showing the types and numbers of atoms present. These formulas provide crucial information for analyzing compounds. A chemical formula consists of:

• Element symbols from the periodic table.
• Subscripts indicating the number of each atom. If there is no subscript, it means only one atom is present.

For example, in sodium sulfate (Na₂SO₄), the formula suggests:
- Two sodium (Na) atoms, one sulfur (S) atom, and four oxygen (O) atoms.
In dinitrogen tetroxide (N₂O₄), it indicates:
- Two nitrogen (N) and four oxygen (O) atoms.
Understanding chemical formulas helps in calculating molecular mass and determining elemental composition. Each compound has its unique formula, dictating its chemical properties and reactions. By interpreting chemical formulas, we can better understand the molecular structure and composition, leading to insights into the compound's characteristics.

Elemental Analysis

Elemental analysis is a fundamental aspect of chemistry used to determine the composition of molecules in a compound. It involves calculating the percentage of each element present in the compound. This analysis follows these basic steps:

• Calculate the total molecular mass of the compound.
• Determine the mass contribution of each element by multiplying its atomic mass by the number of atoms present.
• Compute the percent composition: Divide each element’s mass by the total molecular mass and multiply by 100.

This method aids in understanding the proportion and arrangement of elements within the compound. For instance, in sodium sulfate (Na₂SO₄), one finds:
- The percentage composition of sodium, sulfur, and oxygen by dividing their individual mass by the formula mass and multiplying by 100.
Elemental analysis is crucial in fields like material science and pharmacology, where knowing the exact makeup of a compound impacts its functionality and application. It allows scientists to verify the identity and purity of a substance and to deduce empirical and molecular formulas based on compositional data.