Problem 82 - Chemistry The Molecular Science

Question

Calculate the amount of substance in \(1.00 \mathrm{~g}\) of each compound. (a) \(\mathrm{CH}_{3} \mathrm{OH},\) methanol (b) \(\mathrm{Cl}_{2} \mathrm{CO},\) phosgene, a poisonous gas (c) Ammonium nitrate (d) Magnesium sulfate heptahydrate (Epsom salt) (e) Silver acetate

Step-by-Step Solution

Answer

(a) 0.0312 mol, (b) 0.0101 mol, (c) 0.0125 mol, (d) 0.00406 mol, (e) 0.00600 mol.

Step 1: Calculate Molar Mass of Methanol \((\mathrm{CH}_3\mathrm{OH})\)

Methanol has one carbon, four hydrogen, and one oxygen atom. Calculate using: \( \text{Molar mass} = 12.01 + 4 \times 1.01 + 16.00 = 32.05 \, \mathrm{g/mol} \).

Step 2: Determine Moles of Methanol

Using the formula: \( \mathrm{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.00}{32.05} \approx 0.0312 \, \mathrm{mol}\).

Step 3: Calculate Molar Mass of Phosgene \((\mathrm{Cl}_2\mathrm{CO})\)

Phosgene contains two chlorine, one carbon, and one oxygen atom. Calculate using: \( \text{Molar mass} = 2 \times 35.45 + 12.01 + 16.00 = 98.91 \, \mathrm{g/mol} \).

Step 4: Determine Moles of Phosgene

Using the formula: \( \mathrm{moles} = \frac{1.00}{98.91} \approx 0.0101 \, \mathrm{mol} \).

Step 5: Calculate Molar Mass of Ammonium Nitrate \((\mathrm{NH}_4\mathrm{NO}_3)\)

Ammonium nitrate has two nitrogen, four hydrogen, and three oxygen atoms. Calculate using: \( \text{Molar mass} = 2 \times 14.01 + 4 \times 1.01 + 3 \times 16.00 = 80.05 \, \mathrm{g/mol} \).

Step 6: Determine Moles of Ammonium Nitrate

Using the formula: \( \mathrm{moles} = \frac{1.00}{80.05} \approx 0.0125 \, \mathrm{mol} \).

Step 7: Calculate Molar Mass of Magnesium Sulfate Heptahydrate \((\mathrm{MgSO}_4 \cdot 7\mathrm{H}_2\mathrm{O})\)

The molar mass includes \(\mathrm{MgSO}_4\) and 7 water molecules. Calculate: \( \text{Molar mass} = 24.31 + 32.07 + 4 \times 16.00 + 7 \times (2 \times 1.01 + 16.00) = 246.47 \, \mathrm{g/mol} \).

Step 8: Determine Moles of Magnesium Sulfate Heptahydrate

Using the formula: \( \mathrm{moles} = \frac{1.00}{246.47} \approx 0.00406 \, \mathrm{mol} \).

Step 9: Calculate Molar Mass of Silver Acetate \((\mathrm{C}_2\mathrm{H}_3\mathrm{AgO}_2)\)

Silver acetate contains two carbon, three hydrogen, one silver, and two oxygen atoms. Calculate: \( \text{Molar mass} = 2 \times 12.01 + 3 \times 1.01 + 107.87 + 2 \times 16.00 = 166.91 \, \mathrm{g/mol} \).

Step 10: Determine Moles of Silver Acetate

Using the formula: \( \mathrm{moles} = \frac{1.00}{166.91} \approx 0.00600 \, \mathrm{mol} \).

Key Concepts

Mole Concept

The mole is a fundamental concept in chemistry, often used as a bridge between the atomic scale and the macroscopic world. It helps chemists quantify substances and make calculations based on a number of particles. One mole is defined as exactly 6.022 x 10^23 of any given entity, be it atoms, molecules, or ions. This number, known as Avogadro's number, provides a simple way to transition between the atomic scale and more practical quantities of chemical substances.

When dealing with chemical compounds, the mole concept allows us to calculate the mass of one mole (molar mass) of a compound by summing the individual atomic masses of all elements in the compound's formula. This approach standardizes the way we measure chemical amounts, allowing us to predict how substances will react with each other. The mole concept is crucial in stoichiometric calculations, allowing for accurate measurement to synthesize chemicals or to quantitatively analyze reactions.

Chemical Compounds

Chemical compounds consist of two or more different elements that are chemically bonded together in fixed proportions. These compounds can be categorized into distinct types such as molecular compounds and salts, based on how the atoms are held together. Understanding the structure and composition of chemical compounds is vital to determine their properties and reactions.

For instance, methanol (\(\mathrm{CH}_3\mathrm{OH}\)) comprises carbon, hydrogen, and oxygen, making it an alcohol. Each element contributes to its physical and chemical properties. Similarly, phosgene (\(\mathrm{Cl}_2\mathrm{CO}\)), with its composition of chlorine, carbon, and oxygen, is a toxic gas with industrial applications. The molar mass of these compounds can be calculated by summing the atomic masses of all constituent atoms, which is essential for converting between mass and moles in chemical calculations.

The ability to recognize and analyze chemical compounds is important for predicting reactions, understanding material properties, and for applications across various scientific fields.

Moles Calculation

Moles calculation involves determining the number of moles of a substance from a given mass using the compound's molar mass. This is a fundamental skill in chemistry that allows you to quantify a substance in terms of moles, which are more relevant for chemical reactions.

To perform moles calculation, use the formula:

• Moles = Mass of substance (g) / Molar mass of the compound (g/mol)

For example, if you have 1.00 g of methanol with a molar mass of 32.05 g/mol, the number of moles is approximately 0.0312 mol. This method can be applied to any compound with known molar mass to find the quantity in moles.

Understanding moles and their calculation is crucial for performing stoichiometric calculations, which involve the ratios of reactants and products in a chemical reaction. This ensures reactions are balanced and helps in accurately predicting the yield of chemical processes.