Problem 33 - Chemistry Matter and Change

Question

Challenge Calculate the number of moles of hydrogen atoms in \(1.15 \times 10^{1}\) mol of water. Express the answer in scientific notation.

Step-by-Step Solution

Answer

The number of moles of hydrogen atoms in \(1.15 \times 10^1\) mol of water is \(2.30 \times 10^1\) mol.

Step 1: Understand the chemical formula of water

Water has the chemical formula H2O, which means that each molecule of water consists of two hydrogen atoms (H) and one oxygen atom (O).

Step 2: Calculate the number of moles of hydrogen atoms in the given amount of water

Given that there are 1.15 x 10^1 mol of water, and each molecule of water contains two hydrogen atoms: Number of moles of hydrogen atoms = 2 x moles of water = 2 x (1.15 x 10^1 mol)

Step 3: Express the result in scientific notation

Multiply the number of moles of water by 2: 2 x 1.15 x 10^1 = 2.30 x 10^1 The number of moles of hydrogen atoms in 1.15 x 10^1 mol of water is 2.30 x 10^1 mol, which is the answer expressed in scientific notation.

Key Concepts

Molecules

To begin our exploration of chemical calculations, let's delve into the building blocks known as molecules. Every substance around us is composed of molecules, which are the smallest units of a chemical compound. Molecules are made up of two or more atoms that are bonded together.

• Atoms can belong to the same element, such as two oxygen atoms forming an oxygen molecule ( O_2 ), or different elements, like in water ( H_2O ).
• The chemical formula represents the types and numbers of atoms in a molecule. For example, water's chemical formula is H_2O , indicating each molecule contains two hydrogen atoms and one oxygen atom.

In chemical reactions, we often discuss molecules in large quantities due to their incredibly small size. This is where the concept of moles comes into play, helping us count these enormous numbers in a practical way.

Moles

Transitioning from the microscopic world of molecules, we need a way to count them efficiently. This is where the concept of moles, a fundamental unit in chemistry, is used. A mole provides a bridge between atoms or molecules and grams, allowing chemists to weigh out quantities they can work with.

• Avogadro's number, 6.022 imes 10^{23} , defines the number of atoms or molecules in one mole of a substance.
• Knowing the moles of a compound allows us to infer the number of actual atoms or molecules present.
• For water ( H_2O ), calculating moles helps us determine the quantity of specific atoms, such as hydrogen, by multiplying its moles by the number of atoms per molecule.

Understanding moles is essential for converting mass to molecules and vice versa, and it's widely applied in stoichiometry to predict the proportions of elements involved in chemical reactions.

Scientific Notation

When dealing with very large or very small quantities in chemistry, scientific notation is an invaluable tool. It simplifies the way we deal with numbers, making calculations much more manageable.

• Scientific notation expresses numbers as a product of a number (between 1 and 10) and a power of 10. For example, 1.15 imes 10^1 represents 11.5 in standard decimal form.
• It's particularly useful for representing incredibly small or large values, such as the number of molecules in moles or the masses of atoms.
• In the exercise example, scientific notation makes it easier to express the large number of moles of hydrogen atoms, providing a streamlined way to handle and interpret data.

Mastering scientific notation is critical for working accurately in chemical calculations, ensuring precision and ease in interpreting significant figures across diverse calculations.