Problem 23 - Chemistry The Central Science

Question

Determine the formula weights of each of the following compounds: (a) nitric acid, HNO \(_{3} ;\) (b) \(\mathrm{KMnO}_{4} ;\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) (d) quartz, SiO \(_{2} ;\) (e) gallium sulfide, (f) chromium(III) sulfate, (g) phosphorus trichloride.

Step-by-Step Solution

Answer

The formula weights of the given compounds are as follows: (a) HNO₃: 63.02 g/mol, (b) KMnO₄: 158.04 g/mol, (c) Ca₃(PO₄)₂: 310.18 g/mol, (d) SiO₂: 60.09 g/mol, (e) Ga₂S₃: 235.65 g/mol, (f) Cr₂(SO₄)₃: 392.21 g/mol, and (g) PCl₃: 137.32 g/mol.

Step 1: Nitric Acid (HNO₃)

First, find the molecular weights of H, N, and O from the periodic table: H = 1.01, N = 14.01, O = 16.00. Now, calculate the formula weight for HNO₃: 1(1.01) + 1(14.01) + 3(16.00) = 1.01 + 14.01 + 48.00 = 63.02 g/mol.

Step 2: Potassium Permanganate (KMnO₄)

Find the molecular weights of K, Mn, and O from the periodic table: K = 39.10, Mn = 54.94, O = 16.00. Now, calculate the formula weight for KMnO₄: 1(39.10) + 1(54.94) + 4(16.00) = 39.10 + 54.94 + 64.00 = 158.04 g/mol.

Step 3: Calcium Phosphate (Ca₃(PO₄)₂)

Find the molecular weights of Ca, P, and O from the periodic table: Ca = 40.08, P = 30.97, O = 16.00. Now, calculate the formula weight for Ca₃(PO₄)₂: 3(40.08) + 2(1(30.97) + 4(16.00)) = 120.24 + 2(30.97 + 64.00) = 120.24 + 2(94.97) = 120.24 + 189.94 = 310.18 g/mol.

Step 4: Quartz (SiO₂)

Find the molecular weights of Si and O from the periodic table: Si = 28.09, O = 16.00. Now, calculate the formula weight for SiO₂: 1(28.09) + 2(16.00) = 28.09 + 32.00 = 60.09 g/mol.

Step 5: Gallium Sulfide (Ga₂S₃)

Find the molecular weights of Ga and S from the periodic table: Ga = 69.72, S = 32.07. Now, calculate the formula weight for Ga₂S₃: 2(69.72) + 3(32.07) = 139.44 + 96.21 = 235.65 g/mol.

Step 6: Chromium(III) Sulfate (Cr₂(SO₄)₃)

Find the molecular weights of Cr, S, and O from the periodic table: Cr = 52.00, S = 32.07, O = 16.00. Now, calculate the formula weight for Cr₂(SO₄)₃: 2(52.00) + 3(1(32.07) + 4(16.00)) = 104.00 + 3(32.07+64.00) = 104.00 + 3(96.07) = 104.00 + 288.21 = 392.21 g/mol.

Step 7: Phosphorus Trichloride (PCl₃)

Find the molecular weights of P and Cl from the periodic table: P = 30.97, Cl = 35.45. Now, calculate the formula weight for PCl₃: 1(30.97) + 3(35.45) = 30.97 + 106.35 = 137.32 g/mol. In conclusion, we have calculated the formula weights for all the given compounds: - Nitric Acid (HNO₃): 63.02 g/mol - Potassium Permanganate (KMnO₄): 158.04 g/mol - Calcium Phosphate (Ca₃(PO₄)₂): 310.18 g/mol - Quartz (SiO₂): 60.09 g/mol - Gallium Sulfide (Ga₂S₃): 235.65 g/mol - Chromium(III) Sulfate (Cr₂(SO₄)₃): 392.21 g/mol - Phosphorus Trichloride (PCl₃): 137.32 g/mol

Key Concepts

Molecular Weight

Molecular weight, often referred to as molecular mass, is the sum of the atomic weights of all atoms in a molecule. Understanding molecular weight is crucial for fields like chemistry and biochemistry because it helps us compare different compounds and predicts their behaviors in reactions and solutions.

When calculating the molecular weight, the first step is to identify the elements present in the compound and find their respective atomic weights using the periodic table.

• For example, for nitric acid (HNO₃), you'll combine the weights of hydrogen (H = 1.01), nitrogen (N = 14.01), and oxygen (O = 16.00).
• The molecular weight is calculated by multiplying each elemental atomic weight by the number of times the element appears in the molecule and summing all these values.

Hence, for nitric acid: \[ 1(1.01) + 1(14.01) + 3(16.00) = 63.02 \, \text{g/mol} \] Knowing molecular weights is essential in many scientific calculations and applications, such as determining how much of a substance you need to mix for a chemical reaction.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. This concept stems from the law of conservation of mass, where the total mass of reactants equals the total mass of products.

Stochastic calculations often start with balanced chemical equations and molecular weights to find out exactly how much of one substance will react with another, or what amount of product will result from a certain quantity of reactant. It provides a quantitative relationship between substances as they undergo chemical changes.

• For instance, in the equation for the synthesis of water \(2H_2 + O_2 \to 2H_2O\), stoichiometry tells us that two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of water.
• Using stoichiometry, you could also calculate how much water you end up with if you started with 8 grams of hydrogen and an excess of oxygen.

Understanding stoichiometry helps in predicting yields in chemical reactions, which is crucial for efficient resource usage in industrial and laboratory settings.

Chemical Compounds

Chemical compounds are made from the atoms of different elements combined in fixed proportions. A compound’s characteristics differ essentially from its constituent elements, as new properties emerge through their chemical bonding.

Compounds can be categorized based on the types of bonds between their constituent atoms: ionic, covalent, or metallic.

• Ionic compounds, like calcium phosphate (Ca₃(PO₄)₂), form when atoms transfer electrons to achieve stable electron configurations, typically between metals and non-metals.
• Covalent compounds, on the other hand, involve the sharing of electron pairs between atoms, such as phosphorus trichloride (PCl₃).

Identifying and understanding the types of chemical compounds allow chemists to predict their behavior in reactions, their reactivity, and their potential uses in various applications.

Periodic Table

The periodic table is an organized chart that displays all known chemical elements. It's a fundamental tool for chemists as it provides essential information needed for calculating molecular weights and figuring out electron configurations and chemical properties.

Each element on the table is listed by its atomic number, which represents the number of protons in its nucleus, and its atomic weight, which is its weighted average mass.

• The arrangement of elements in the periodic table is by increasing atomic number. This layout groups elements with similar chemical properties into vertical columns known as groups.
• For instance, elements in the same group like fluorine (F) and chlorine (Cl) have similar chemical properties because they have the same number of electrons in their outermost shell.

Using the periodic table, we can deduce valuable insights about an element's behavior and bonding capacity, which aids greatly in the study and application of chemical reactions and compounds.