Question

How many moles are present in \(100 \mathrm{~g}\) quantities of each of the following? (a) \(\mathrm{CaCO}_{3}\), (b) \(\mathrm{H}_{2} \mathrm{O}\), (c) \(\mathrm{HCl}\), (d) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} ?\)

Short answer

In 100 g quantities, there are: \(1 \: \text{mol of} \: \mathrm{CaCO}_{3}\), \(5.56 \: \text{mol of} \: \mathrm{H}_{2} \mathrm{O}\), \(2.74 \: \text{mol of} \: \mathrm{HCl}\), and \(0.292 \: \text{mol of} \: \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\).

Step-by-step solution

Molar Mass Calculation

Calculate the molar mass of each substance using the periodic table. (a) For CaCO3: Molar mass = (40 g/mol for Ca) + (12 g/mol for C) + (3×16 g/mol for O) = 100 g/mol (b) For H2O: Molar mass = (2×1 g/mol for H) + (16 g/mol for O) = 18 g/mol (c) For HCl: Molar mass = (1 g/mol for H) + (35.5 g/mol for Cl) = 36.5 g/mol (d) For Al2(SO4)3: Molar mass = (2×27 g/mol for Al) + (3×[32 g/mol for S + 4×(16 g/mol for O)]) = 342 g/mol

Number of Moles Calculation

Calculate the number of moles for each substance using their molar masses. (a) Moles of CaCO3 = (100 g) / (100 g/mol) = 1 mol (b) Moles of H2O = (100 g) / (18 g/mol) = 5.56 mol (c) Moles of HCl = (100 g) / (36.5 g/mol) = 2.74 mol (d) Moles of Al2(SO4)3 = (100 g) / (342 g/mol) = 0.292 mol So, there are 1 mol of CaCO3, 5.56 mol of H2O, 2.74 mol of HCl, and 0.292 mol of Al2(SO4)3 present in 100 g quantities of each substance.

Key concepts

Understanding Molar Mass

Molar mass is an essential concept in chemistry, representing the mass of one mole of a substance. It's expressed in grams per mole (g/mol). When you look at a compound, its molar mass reflects the sum of the masses of all the atoms it contains.
To find the molar mass, we use the periodic table. Each element has a unique atomic mass, usually listed under its symbol. For example, calcium (Ca) has an atomic mass of 40 g/mol, while carbon (C) is 12 g/mol.
Add the atomic masses of all atoms in a compound to find its total molar mass. In the case of

• CaCO₃ (1 Ca, 1 C, 3 O): The molar mass is 40 + 12 + (3×16) = 100 g/mol.
• H₂O (2 H, 1 O): 2×1 + 16 = 18 g/mol.
• HCl (1 H, 1 Cl): 1 + 35.5 = 36.5 g/mol.
• Al₂(SO₄)₃ (2 Al, 3 S, 12 O): (2×27) + 3×(32 + 4×16) = 342 g/mol.

Calculation Method for Finding Moles

To determine the number of moles present in a specific quantity of a substance, we use the relationship between mass and molar mass. The formula used is:Number of moles = \( \frac{\text{Mass of substance (grams)}}{\text{Molar mass (g/mol)}} \).
This formula allows us to convert a given mass into moles by dividing the mass by the molar mass. This conversion is central to many chemistry problems since moles connect the relative amounts of reactants and products in a chemical reaction.
Consider

• 100 g of CaCO₃ with molar mass 100 g/mol results in \( \frac{100}{100} = 1 \) mole.
• For H₂O, with 100 g and a molar mass of 18 g/mol, \( \frac{100}{18} = 5.56 \) moles.
• In the case of HCl, \( \frac{100}{36.5} = 2.74 \) moles.
• Finally, for Al₂(SO₄)₃, \( \frac{100}{342} = 0.292 \) moles.

This process shows how understanding molar mass facilitates the calculation of moles, a fundamental step in stoichiometry.

Introduction to Stoichiometry

Stoichiometry is the branch of chemistry that involves calculating the relationships between the reactants and products in chemical reactions. It deeply relies on the concept of moles and molar mass for precise measurements.
In stoichiometry, we use balanced chemical equations. These equations illustrate how molecules interact, create, and transform into products. Each molecule corresponds to a specific number of moles, essential for predicting quantities of different substances involved.
Consider a simple reaction:

• If 1 mole of a compound A reacts with 2 moles of B, knowing the moles helps us determine the amount of product formed.
• Using stoichiometry, we can find out how much of each reactant is needed to create a desired amount of product.
• This method aids chemists in scaling reactions up or down, maintaining economy and efficiency in real-world applications.

The process of stoichiometry demonstrates how calculations are used to solve practical problems in chemistry.

Using the Periodic Table for Molar Mass

The periodic table is an invaluable tool for chemists. It provides crucial information for calculating molar mass, a necessary step in mole calculations. Each element on the table is listed with its atomic number, symbol, and atomic mass, among other properties.

• The atomic mass reflects the mass of an atom of an element. This is the average mass number because it accounts for all isotopes of the element occurring naturally.
• For our calculations, we use the atomic mass to determine the molar mass of compounds by adding the masses of each constituent atom.
• This process is straightforward: locate the element, find its atomic mass, and perform the necessary addition.

For example, using the elements calcium (Ca), carbon (C), oxygen (O), hydrogen (H), and chlorine (Cl), you can calculate the molar masses of different compounds accurately.
Therefore, mastering the use of the periodic table is vital for effectively performing calculations related to moles and molar mass.