Problem 131 - Chemistry Matter and Change

Question

Determine the molar mass of each compound. a. nitric acid \(\left(\mathrm{HNO}_{3}\right)\) b. ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) c. zinc oxide \((\mathrm{ZnO})\) d. cobalt chloride \(\left(\mathrm{CoCl}_{2}\right)\)

Step-by-Step Solution

Answer

The molar masses of the compounds are: a. Nitric acid (HNO₃) = 63.02 g/mol b. Ammonium nitrate (NH₄NO₃) = 80.06 g/mol c. Zinc oxide (ZnO) = 81.38 g/mol d. Cobalt chloride (CoCl₂) = 129.83 g/mol

Step 1: Identify the elements and their respective atomic masses in each compound

Consult a periodic table to determine the atomic weight of each element present in the compound. a. For nitric acid (HNO₃): Hydrogen (H): 1.01 g/mol Nitrogen (N): 14.01 g/mol Oxygen (O): 16.00 g/mol b. For ammonium nitrate (NH₄NO₃): Hydrogen (H): 1.01 g/mol Nitrogen (N): 14.01 g/mol Oxygen (O): 16.00 g/mol c. For zinc oxide (ZnO): Zinc (Zn): 65.38 g/mol Oxygen (O): 16.00 g/mol d. For cobalt chloride (CoCl₂): Cobalt (Co): 58.93 g/mol Chlorine (Cl): 35.45 g/mol

Step 2: Calculate the molar mass of each compound

Multiply the atomic weight of each element by the number of atoms of that element in the compound and sum the total weights. a. Molar mass of nitric acid (HNO₃): \(1 \times (1.01 \text{ g/mol}) + 1 \times (14.01 \text{ g/mol}) + 3 \times (16.00 \text{ g/mol}) = 1.01 + 14.01 + 48.00 = 63.02 \text{ g/mol}\) b. Molar mass of ammonium nitrate (NH₄NO₃): \(4 \times (1.01 \text{ g/mol}) + 2 \times (14.01 \text{ g/mol}) + 3 \times (16.00 \text{ g/mol}) = 4.04 + 28.02 + 48.00 = 80.06 \text{ g/mol}\) c. Molar mass of zinc oxide (ZnO): \(1 \times (65.38 \text{ g/mol}) + 1 \times (16.00 \text{ g/mol}) = 65.38 + 16.00 = 81.38 \text{ g/mol}\) d. Molar mass of cobalt chloride (CoCl₂): \(1 \times (58.93 \text{ g/mol}) + 2 \times (35.45 \text{ g/mol}) = 58.93 + 70.90 = 129.83 \text{ g/mol}\)

Step 3: Present the molar mass of each compound

The molar masses of each compound are as follows: a. Molar mass of nitric acid (HNO₃) = 63.02 g/mol b. Molar mass of ammonium nitrate (NH₄NO₃) = 80.06 g/mol c. Molar mass of zinc oxide (ZnO) = 81.38 g/mol d. Molar mass of cobalt chloride (CoCl₂) = 129.83 g/mol

Key Concepts

Atomic Weight

Understanding atomic weight is crucial when calculating the molar mass of a compound. Atomic weight, often termed relative atomic mass, is a dimensionless quantity that expresses how heavy an atom of a chemical element is compared to a twelfth of the mass of a carbon-12 atom.

It is a weighted average of the isotopes of an element as found naturally on Earth. Each element on the periodic table has its own unique atomic weight. For instance, in the exercise provided, hydrogen (H) has an atomic weight of approximately 1.01, indicating that it is very light relative to other elements. On the other hand, zinc (Zn) has a much higher atomic weight of 65.38, reflecting its greater mass per atom.

When you look up these values on the periodic table, you are gathering the necessary data to compute the molar mass of chemical compounds. Remember, the atomic weight is an essential building block for such calculations.

Chemical Compounds

In chemistry, a chemical compound is a substance composed of two or more different elements that are chemically bonded together. Compounds have unique properties that are distinct from the elements they are made of. For example, water (H₂O) has completely different characteristics from its constituent elements, hydrogen and oxygen.

In the step-by-step solution for finding the molar mass, we accounted for all atoms in a given compound. The compounds ranged from simple diatomic molecules like zinc oxide (ZnO) to more complex ones like ammonium nitrate (NH₄NO₃). The key to solving these problems lies in correctly determining the formula of the compounds, identifying the elements involved, and knowing how many atoms of each element are present in one molecule of the compound. Each atom contributes to the total molar mass based on its atomic weight and the number of times it appears in the molecule.

Periodic Table

The periodic table is a comprehensive chart that organizes all the known chemical elements in an informative and systematic array. Elements are arranged from left to right and top to bottom in order of increasing atomic number. The table is a key tool for students and scientists alike, as it provides a wealth of information about the elements, including atomic numbers, element symbols, electron configurations, and importantly for our purposes, atomic weights.

When calculating molar masses, the periodic table becomes your best reference, as it shows the atomic weight of every element. Using the periodic table, you can identify the constituent elements of chemical compounds and their respective atomic weights which is the first step to determine the molar mass of a compound. Moreover, the periodic table hints at the chemical behavior of elements and how they might combine to form compounds, guiding us toward a better understanding of molecular structures.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. For stoichiometry, the molar mass is a bridge between the mass of a substance and the number of particles or moles present in that mass. It allows us to convert grams to moles, a critical conversion in chemical calculations.

Calculating molar mass directly applies stoichiometric principles. As demonstrated in the solutions, we combine the atomic weights of the elements according to the number of atoms of each in the compound's formula. This process essentially counts the 'amount' of an element in a molecule in mole terms. Stoichiometry could further be extended to balance chemical equations, predict the yield of products, and calculate reactant requirements. Without molar mass as a cornerstone of stoichiometry, predictions in chemical reactions would be near impossible to quantify.