Question

Calculate the percent by mass of the element mentioned first in the formulas for each of the following compounds. a. sodium azide, \(\mathrm{NaN}_{3}\) b. copper(II) sulfate, \(\mathrm{CuSO}_{4}\) c. gold(III) chloride, \(\mathrm{AuCl}_{3}\) d. silver nitrate, \(\mathrm{AgNO}_{3}\) e. rubidium sulfate, \(\mathrm{Rb}_{2} \mathrm{SO}_{4}\) f. sodium chlorate, \(\mathrm{NaClO}_{3}\) g. nitrogen triiodide, \(\mathrm{NI}_{3}\) h. cesium bromide, \(\mathrm{CsBr}\)

Short answer

a. Sodium Azide, \(\mathrm{NaN}_{3}\): 35.37% b. Copper(II) Sulfate, \(\mathrm{CuSO}_{4}\): 39.84% c. Gold(III) Chloride, \(\mathrm{AuCl}_{3}\): 65.86% d. Silver Nitrate, \(\mathrm{AgNO}_{3}\): 64.45% e. Rubidium Sulfate, \(\mathrm{Rb}_{2} \mathrm{SO}_{4}\): 60.98% f. Sodium Chlorate, \(\mathrm{NaClO}_{3}\): 21.62% g. Nitrogen Triiodide, \(\mathrm{NI}_{3}\): 3.54% h. Cesium Bromide, \(\mathrm{CsBr}\): 72.17%

Step-by-step solution

Find the molar mass of \(\mathrm{NaN}_{3}\)

To find the molar mass, add the molar masses of the elements in the compound. In this case: Molar mass of \(\mathrm{NaN}_{3}\) = (1 × molar mass ofNa) + (3 × molar mass of N) Molar mass of \(\mathrm{NaN}_{3}\) = (1 × 22.99 g/mol) + (3 × 14.01 g/mol) Molar mass of \(\mathrm{NaN}_{3}\) = 65.01 g/mol

Calculate the percent by mass of sodium in \(\mathrm{NaN}_{3}\)

Percent by mass = (Mass of Na / Molar Mass of \(\mathrm{NaN}_{3}\)) × 100 Percent by mass = (22.99 g/mol / 65.01 g/mol) × 100 Percent by mass = 35.37% b. Copper(II) Sulfate, \(\mathrm{CuSO}_{4}\)

Find the molar mass of \(\mathrm{CuSO}_{4}\)

Molar mass of \(\mathrm{CuSO}_{4}\) = (1 x molar mass of Cu) + (1 x molar mass of S) + (4 x molar mass of O) Molar mass of \(\mathrm{CuSO}_{4}\) = (1 x 63.55 g/mol) + (1 x 32.07 g/mol) + (4 x 16.00 g/mol) Molar mass of \(\mathrm{CuSO}_{4}\) = 159.62 g/mol

Calculate the percent by mass of copper in \(\mathrm{CuSO}_{4}\)

Percent by mass = (Mass of Cu / Molar Mass of \(\mathrm{CuSO}_{4}\)) × 100 Percent by mass = (63.55 g/mol / 159.62 g/mol) × 100 Percent by mass = 39.84% Continue with the same steps for the remaining compounds: c. Gold(III) Chloride, \(\mathrm{AuCl}_{3}\) Molar Mass: 303.33 g/mol Percent by mass of Au: 65.86% d. Silver Nitrate, \(\mathrm{AgNO}_{3}\) Molar Mass: 169.88 g/mol Percent by mass of Ag: 64.45% e. Rubidium Sulfate, \(\mathrm{Rb}_{2} \mathrm{SO}_{4}\) Molar Mass: 378.94 g/mol Percent by mass of Rb: 60.98% f. Sodium Chlorate, \(\mathrm{NaClO}_{3}\) Molar Mass: 106.44 g/mol Percent by mass of Na: 21.62% g. Nitrogen Triiodide, \(\mathrm{NI}_{3}\) Molar Mass: 394.72 g/mol Percent by mass of N: 3.54% h. Cesium Bromide, \(\mathrm{CsBr}\) Molar Mass: 212.81 g/mol Percent by mass of Cs: 72.17%

Key concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the substances participating in chemical reactions. It involves calculating the amounts of reactants and products based on balanced chemical equations.

When calculating percent composition by mass, stoichiometry comes into play because you need to understand the relation between the mass of individual elements and the overall molar mass of compounds. For instance, in a chemical reaction, stoichiometry helps you determine how much sodium azide (\(\mathrm{NaN}_{3}\)) is needed to produce a certain amount of gas, which could be pivotal in automotive airbag systems.

Getting familiar with stoichiometry allows you to grasp not only how the elements combine but also how to translate this into practical applications such as calculating yields of reactions, understanding limiting reagents, and analyzing empirical and molecular formulas.

Molar Mass Calculation

The molar mass of a substance is the mass in grams of one mole of that substance. One mole corresponds to Avogadro's number (\(6.022 \times 10^{23}\)) of particles, whether they are atoms, molecules, ions, or electrons.

For molar mass calculation, as seen in the step-by-step solution, you add the masses of all the atoms in a molecule. The mass of each element can be found on the periodic table and is expressed in atomic mass units (amu), where 1 amu equals 1 gram per mole (g/mol).

Importance of Accurate Molar Mass in Calculations

Getting the exact molar mass is crucial for precise stoichiometric calculations. Inaccurate molar mass leads to incorrect percent compositions, which can drastically affect the outcomes of experiments and industrial processes such as pharmaceutical compound formulation where precise ingredient ratios are essential.

Chemical Formulas

Chemical formulas represent the types and numbers of atoms in a substance. For example, \(\mathrm{CuSO}_{4}\) represents copper(II) sulfate, with 'Cu' standing for one atom of copper, 'S' for sulfur, and 'O' for oxygen. The subscript '4' after oxygen indicates there are four oxygen atoms in one molecule of copper(II) sulfate.

Understanding chemical formulas is crucial for interpreting the composition of compounds, performing molar mass calculations, and eventually determining percent compositions. Formulas indicate the ratios of elements, which help in identifying the proportions of each element within a compound. This information serves as the foundation for calculating the percent by mass. In educational settings, clear understanding of chemical formulas can facilitate learning and application of advanced topics, like reaction mechanisms and molecular geometry.