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

a. 63.02 g/mol, b. 80.05 g/mol, c. 81.38 g/mol, d. 129.83 g/mol

Step 1: Find Atomic Masses

Locate the atomic masses of the elements involved. You can find these on the periodic table. For this exercise, the atomic masses are approximately: H = 1.01 amu, N = 14.01 amu, O = 16.00 amu, Zn = 65.38 amu, Co = 58.93 amu, and Cl = 35.45 amu.

Step 2: Calculate Molar Mass of Nitric Acid

For nitric acid \(\mathrm{HNO}_{3}\), add the atomic masses of hydrogen, nitrogen, and three oxygens: \(1.01 + 14.01 + 3 \times 16.00 = 63.02\) amu.

Step 3: Calculate Molar Mass of Ammonium Nitrate

For ammonium nitrate \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), add the atomic masses of one nitrogen, four hydrogens, one nitrogen, and three oxygens: \(14.01 + 4 \times 1.01 + 14.01 + 3 \times 16.00 = 80.05\) amu.

Step 4: Calculate Molar Mass of Zinc Oxide

For zinc oxide (ZnO), add the atomic masses of zinc and oxygen: \(65.38 + 16.00 = 81.38\) amu.

Step 5: Calculate Molar Mass of Cobalt Chloride

For cobalt chloride \(\mathrm{CoCl}_{2}\), add the atomic masses of cobalt and two chlorines: \(58.93 + 2 \times 35.45 = 129.83\) amu.

Key Concepts

Atomic Mass

Atomic mass is a fundamental concept in chemistry that signifies the mass of a single atom of a chemical element. This value is commonly expressed in atomic mass units (amu). For example, hydrogen has an atomic mass of approximately 1.01 amu.
Knowing the atomic masses of elements allows us to calculate the molar mass of compounds, which is crucial for chemical reactions. The periodic table is a helpful tool, listing the atomic masses of all elements. Here are a few examples:

• Hydrogen (H): 1.01 amu
• Nitrogen (N): 14.01 amu
• Oxygen (O): 16.00 amu
• Zinc (Zn): 65.38 amu
• Cobalt (Co): 58.93 amu
• Chlorine (Cl): 35.45 amu

Understanding atomic mass helps determine the weight of molecules and is essential for tasks such as calculating the molar mass of compounds.

Nitric Acid

Nitric acid is a highly corrosive and strong mineral acid with the formula \(\mathrm{HNO}_{3}\).It consists of three main components: hydrogen, nitrogen, and oxygen.
The molecular arrangement includes one hydrogen atom, one nitrogen atom, and three oxygen atoms.
Calculating its molar mass involves adding together the atomic masses of each component:

• Hydrogen: 1.01 amu
• Nitrogen: 14.01 amu
• Oxygen (three atoms): 3 \times 16.00 = 48.00 amu

Adding these gives us a molar mass of 63.02 amu for nitric acid. Understanding its composition and molar mass is crucial for various industrial applications, including manufacturing fertilizers and explosives.

Ammonium Nitrate

Ammonium nitrate, with the chemical formula \(\mathrm{NH}_{4} \mathrm{NO}_{3}\),is a compound used extensively in fertilizers and explosives due to its nitrate content.
The formula breaks down into ammonium (\(\mathrm{NH}_{4}^{+}\)) and nitrate (\(\mathrm{NO}_{3}^{-}\)) ions.
To find its molar mass, we add the atomic masses of all the atoms involved:

• Nitrogen (two atoms): 2 \times 14.01 = 28.02 amu
• Hydrogen (four atoms): 4 \times 1.01 = 4.04 amu
• Oxygen (three atoms): 3 \times 16.00 = 48.00 amu

Summing these values, we find the molar mass of ammonium nitrate to be 80.05 amu. This calculation helps in quantifying the compound for agricultural and industrial processes.

Zinc Oxide

Zinc oxide \((\mathrm{ZnO})\)is a compound with diverse applications, from sunscreens to ceramics. It consists of two elements:
zinc and oxygen. Knowing their atomic masses enables precise molar mass calculation:

• Zinc: 65.38 amu
• Oxygen: 16.00 amu

By adding them together, we find the molar mass of zinc oxide to be 81.38 amu.
Understanding this helps formulate products and substances in industries where zinc oxide is a significant component, ensuring correct proportions and functionality.

Cobalt Chloride

Cobalt chloride, \(\mathrm{CoCl}_{2}\),is primarily known for use in humidity detectors and as a precursor to other cobalt compounds. This compound involves cobalt and chlorine atoms.
The formula incorporates one cobalt atom and two chlorine atoms. Here's how to compute its molar mass:

• Cobalt: 58.93 amu
• Chlorine (two atoms): 2 \times 35.45 = 70.90 amu

Summing these calculations provides a molar mass of 129.83 amu for cobalt chloride. These calculations are vital for applications requiring precise chemical compositions and interactions, such as in chemistry labs or industrial processes.