Question

Calculate the percent by mass of the element listed first in the formulas for each of the following compounds. a. methane, \(\mathrm{CH}_{4}\) b. sodium nitrate, \(\mathrm{NaNO}_{3}\) c. carbon monoxide, \(\mathrm{CO}\) d. nitrogen dioxide, \(\mathrm{NO}_{2}\) e. 1 -octanol, \(\mathrm{C}_{8} \mathrm{H}_{18} \mathrm{O}\) f. calcium phosphate, \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) g. 3 -phenylphenol, \(\mathrm{C}_{12} \mathrm{H}_{10} \mathrm{O}\) h. aluminum acetate, \(\mathrm{Al}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{3}\)

Short answer

The percent by mass of the first element in each compound is as follows: a. Methane (CH4) - 75% b. Sodium Nitrate (NaNO3) - 27.06% c. Carbon Monoxide (CO) - 42.86% d. Nitrogen Dioxide (NO2) - 30.43% e. 1-octanol (C8H18O) - 73.85% f. Calcium Phosphate (Ca3(PO4)2) - 38.71% g. 3-phenylphenol (C12H10O) - 84.71% h. Aluminum Acetate (Al(C2H3O2)3) - 13.24%

Step-by-step solution

Identify the needed atomic masses

We retrieve the following atomic masses (rounded) from the periodic table of elements: - Carbon (C): 12 - Hydrogen (H): 1 - Sodium (Na): 23 - Nitrogen (N): 14 - Oxygen (O): 16 - Calcium (Ca): 40 - Phosphorus (P): 31 - Aluminum (Al): 27

Methane (CH4)

Calculate the mass of the compound methane and the percentage of carbon: - Mass of CH4 = 12 + 4(1) = 16 g/mol Percent by mass of Carbon in CH4 = (12/16) × 100 = 75%

Sodium Nitrate (NaNO3)

Calculate the mass of the compound sodium nitrate and the percentage of sodium: - Mass of NaNO3 = 23 + 14 + 3(16) = 85 g/mol Percent by mass of Sodium in NaNO3 = (23/85) × 100 = 27.06%

Carbon Monoxide (CO)

Calculate the mass of the compound carbon monoxide and the percentage of carbon: - Mass of CO = 12 + 16 = 28 g/mol Percent by mass of Carbon in CO = (12/28) × 100 = 42.86%

Nitrogen Dioxide (NO2)

Calculate the mass of the compound nitrogen dioxide and the percentage of nitrogen: - Mass of NO2 = 14 + 2(16) = 46 g/mol Percent by mass of Nitrogen in NO2 = (14/46) × 100 = 30.43%

1-octanol (C8H18O)

Calculate the mass of the compound 1-octanol and the percentage of carbon: - Mass of C_8H_18O = 8(12) + 18(1) + 16 = 130 g/mol Percent by mass of Carbon in C8H18O = (8(12)/130) × 100 = 73.85%

Calcium Phosphate (Ca3(PO4)2)

Calculate the mass of the compound calcium phosphate and the percentage of calcium: - Mass of Ca3(PO4)2 = 3(40) + 2(31 + 4(16)) = 310 g/mol Percent by mass of Calcium in Ca3(PO4)2 = (3(40)/310) × 100 = 38.71%

3-phenylphenol (C12H10O)

Calculate the mass of the compound 3-phenylphenol and the percentage of carbon: - Mass of C12H10O = 12(12) + 10(1) + 16 = 170 g/mol Percent by mass of Carbon in C12H10O = (12(12)/170) × 100 = 84.71%

Aluminum Acetate (Al(C2H3O2)3)

Calculate the mass of the compound aluminum acetate and the percentage of aluminum: - Mass of Al(C2H3O2)3 = 27 + 3(2(12) + 3(1) + 2(16)) = 204 g/mol Percent by mass of Aluminum in Al(C2H3O2)3 = (27/204) × 100 = 13.24% To summarize, the percent by mass for each compound is as follows: a. Methane (CH4) - 75% b. Sodium Nitrate (NaNO3) - 27.06% c. Carbon Monoxide (CO) - 42.86% d. Nitrogen Dioxide (NO2) - 30.43% e. 1 -octanol (C8H18O) - 73.85% f. Calcium Phosphate (Ca3(PO4)2) - 38.71% g. 3 -phenylphenol (C12H10O) - 84.71% h. Aluminum Acetate (Al(C2H3O2)3) - 13.24%

Key concepts

Molecular Mass Calculation

Molecular mass calculation is a crucial step in understanding the composition of chemical compounds. It is the sum of the atomic masses of all the atoms present in a molecule. To calculate the molecular mass:

• Identify each type of atom in the molecule.
• Count the number of each atom.
• Multiply the atomic mass of each type of atom by its quantity.
• Sum the total masses to find the molecular mass of the compound.

The resulting value, typically expressed in grams per mole (g/mol), provides essential information about how much each type of atom contributes to the complete molecule. Let's use methane (\(\text{CH}_{4}\)) as an example: methane has one carbon atom with an atomic mass of 12 and four hydrogen atoms each with an atomic mass of 1. Thus, the molecular mass is 12 + 4(1) = 16 g/mol. This indicates the total mass of methane in one mole, integrating both carbon and hydrogen contributions.

Atomic Mass

Understanding atomic mass is fundamental in the calculation of percent composition and molecular mass. Each chemical element has a unique atomic mass, which is the average mass of an atom of the element measured in atomic mass units (amu). This value reflects the number of protons and neutrons in the atom's nucleus. For example:

• Carbon (C) has an atomic mass of approximately 12 amu.
• Hydrogen (H) has an atomic mass close to 1 amu.
• Oxygen (O) has an atomic mass of about 16 amu.

By using the atomic masses from the periodic table for each atom in a molecule, we can determine the molecular mass of that molecule. Familiarity with atomic masses is essential for students to accurately carry out molecular and percent mass calculations.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more elements. The composition of these compounds is expressed within a chemical formula that provides information about the types and numbers of atoms involved. Understanding these formulas is essential:

• The subscript numbers in a formula show the number of each type of atom in the molecule.
• For instance, in water (\(\text{H}_{2}\text{O}\)), there are two hydrogen atoms and one oxygen atom.
• In carbon monoxide (\(\text{CO}\)), there is one carbon and one oxygen atom.

These formulas allow chemists to calculate both molecular mass and percent composition, providing insight into the relative quantities of each component within the compound. Understanding chemical formulas is crucial for exploring how compounds react and interact with one another.

Step-by-Step Solution

Solving a chemical exercise systematically can help students thoroughly understand the processes involved. Let's revisit the percent composition task from our exercise using a step-by-step approach:

• First, identify the atomic masses needed for each element in the compound using the periodic table.
• Calculate the total molecular mass by adding the atomic masses of its constituent atoms.
• Determine the mass percentage of the element of interest by dividing its atomic mass contribution by the molecular mass and multiplying by 100 to convert the value into a percentage.

By practicing this step-by-step process with different compounds, students become proficient in percent composition calculations. Breaking down problems into manageable steps makes complex chemistry problems easier to understand and solves them methodically, ensuring accurate results every time.