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Atomic weights are crucial for understanding and calculating the molecular weight of chemical compounds. Each element has its own atomic weight, which is the average mass of its atoms typically expressed in grams per mole (g/mol). These values are based on the isotopes of each element and their relative abundance on Earth. Using these atomic weights, we can compute the total molecular weight by summing up the contributions of all the constituent atoms.

An element like carbon (C) has an atomic weight of 12.01 g/mol. Oxygen (O), which is another common element in many compounds, has an atomic weight of 16.00 g/mol. Other important atomic weights include chromium (Cr) at 51.996 g/mol and calcium (Ca) at 40.078 g/mol. These values remain constant and are used universally in chemical calculations.

• Carbon (C): 12.01 g/mol
• Oxygen (O): 16.00 g/mol
• Chromium (Cr): 51.996 g/mol
• Iron (Fe): 55.845 g/mol
• Potassium (K): 39.098 g/mol
• Calcium (Ca): 40.078 g/mol

The atomic weights serve as building blocks that chemists use for precise calculations and predictions related to chemical reactions and molecular compositions.

Chemical compounds are formed when two or more elements combine together in fixed ratios. These compounds have unique properties and chemical formulas that indicate the type and number of atoms involved. Understanding the individiual components of a compound is crucial because it helps in calculating the molecular weight, which is the sum of all atomic weights in the compound.

Let's consider some examples of compounds as given in the original exercise:

• Chromium hexacarbonyl, \({\rm Cr(CO)_6}\), which consists of 1 chromium atom and 6 carbonyl (CO) groups.
• Iron(III) nitrate, \({\rm Fe(NO_3)_3}\), which is composed of 1 iron atom and 3 nitrate (NO_3) groups.
• Potassium dichromate, \({\rm K_2Cr_2O_7}\), made up of 2 potassium, 2 chromium, and 7 oxygen atoms.
• Calcium phosphate, \({\rm Ca_3(PO_4)_2}\), with 3 calcium, 2 phosphorous, and 8 oxygen atoms.

The knowledge of the chemical structure and the number of each type of atom is pivotal to determining the molecular weight and understanding the properties of the compound.

The step-by-step solution for calculating molecular weight involves breaking down the compound into its atomic constituents and using the known atomic weights for calculation. Let's see how this unfolds with the examples:

Step 2: Chromium Hexacarbonyl Calculation
The molecular weight is derived from 1 chromium and 6 carbonyl, \( {\rm CO} \), groups. Each CO group is a combination of one carbon and one oxygen. By adding up these atomic weights, the molecular weight of Cr(CO)₆ becomes:\[molecular\ weight = 1 \times 51.996 + 6 \times (12.01 + 16.00) = 220.06 \, {\rm g/mol}\]

Step 3: Iron(III) Nitrate Calculation
This compound has 1 iron and 3 nitrate, \({\rm NO}_3\), groups. The calculation follows:\[molecular\ weight = 1 \times 55.845 + 3 \times (14.007 + 3 \times 16.00) = 241.86 \, {\rm g/mol}\]

Step 4: Potassium Dichromate Calculation
It consists of 2 potassium, 2 chromium, and 7 oxygen atoms, leading to:\[molecular\ weight = 2 \times 39.098 + 2 \times 51.996 + 7 \times 16.00 = 294.18 \, {\rm g/mol}\]

Step 5: Calcium Phosphate Calculation
This involves 3 calcium, 2 phosphorus, and 8 oxygen atoms:\[molecular\ weight = 3 \times 40.078 + 2 \times 30.974 + 8 \times 16.00 = 310.18 \, {\rm g/mol}\]Following these clear steps helps ensure accuracy and strengthen understanding of molecular weight computation.