Question

What is the mass of \(0.100 \mathrm{~mol}\) of \(\mathrm{Cu}(\mathrm{OH})_{2}\) ?

Short answer

The mass of \(0.100 \mathrm{~mol}\) of \(\mathrm{Cu}(\mathrm{OH})_{2}\) is 9.76 g.

Step-by-step solution

Determine the Atomic Mass of Each Element

First, find the atomic mass of each element present in \(\mathrm{Cu}(\mathrm{OH})_{2}\). For this compound, the atomic mass of copper (Cu) is roughly 63.546 g/mol. For Oxygen (O), it's around 15.999 g/mol, and for Hydrogen (H), it's approximately 1.008 g/mol.

Calculate the Molar Mass of the Compound

To find the molar mass of the compound, add up the atomic masses of all atoms in the compound: Molar mass of Copper Hydroxide = mass of Copper + 2 * (mass of Oxygen + mass of Hydrogen). This is essentially: \(63.546 \mathrm{ g/mol} + 2 \times (15.999 \mathrm{ g/mol} + 1.008 \mathrm{ g/mol})\).

Multiply Moles by the Molar Mass

Since you're trying to find the mass of \(0.100 \mathrm{~mol}\) Copper Hydroxide, multiply the number of moles by the molar mass of the compound.

Key concepts

Understanding Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of an atom of a chemical element. This is usually measured in atomic mass units (amu) or grams per mole (g/mol), which effectively equate due to Avogadro's number. Each element has a unique atomic mass based on the number of protons and neutrons in its nucleus. For instance:

• The atomic mass of Copper (Cu) is approximately 63.546 g/mol.
• Oxygen (O) has an atomic mass of about 15.999 g/mol.
• Hydrogen (H), being the lightest, has an atomic mass of roughly 1.008 g/mol.

Knowing the atomic mass allows us to calculate the molar mass of compounds, like Copper Hydroxide, by summing the atomic masses of its constituents. This is crucial for predicting how compounds will interact in chemical reactions, as described in stoichiometry.

Properties of Copper Hydroxide

Copper Hydroxide, denoted as \(\text{Cu(OH)}_2\), is a fascinating compound made up of copper, oxygen, and hydrogen. It's commonly known for its striking blue color and serves various applications in industries and laboratories. Here's a breakdown of its structure and formula:

• It consists of one copper atom bonded to two hydroxide groups (each an OH unit).
• This results in the molecular formula \(\text{Cu(OH)}_2\).
• Given the atomic masses (Cu: 63.546 g/mol, O: 15.999 g/mol, H: 1.008 g/mol), we calculate its molar mass as: \(63.546 + 2 \times (15.999 + 1.008)\).

Knowing these details about Copper Hydroxide helps in calculating the mass of given moles in practical problems. The molar mass calculation is straightforward using these atomic masses, making it manageable to move on to applications in stoichiometry.

The Role of Stoichiometry in Chemistry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It’s pivotal for ensuring that reactions are balanced and occur in the right proportions. When dealing with stoichiometric calculations, we often use the following steps:

• Determine the balanced chemical equation of the reaction at hand.
• Use the molar mass to convert moles to mass or vice-versa.
• Establish the mole ratio between reactants and products as described by the coefficients in the balanced equation.

In the context of our problem, once we have the molar mass of Copper Hydroxide \(\text{Cu(OH)}_2\), we multiply it by the number of moles given (0.100 mol). This relates to stoichiometry as it allows us to predict the mass that results from a certain number of moles based on atomic mass ratios, exemplifying the exactness stoichiometry brings to chemistry.