Problem 16 - Chemistry

Question

How many grams of gold (Au) are there in 15.3 moles of Au?

Step-by-Step Solution

Answer

The mass of 15.3 moles of gold is 3013.1 grams.

Step 1: Understand the Problem

We need to find out the weight in grams of 15.3 moles of gold. From the periodic table, we know that the molar mass of gold (Au) is 197 grams/mole.

Step 2: Use the Conversion Factor

We will use the molar mass of gold as a conversion factor. The conversion factor is 197 grams/mole. This means that one mole of gold has a mass of 197 grams.

Step 3: Perform the Calculation

To get the total mass, multiply the number of moles by the molar mass. That is, \( 15.3 \, moles \times 197 \, \frac{grams}{mole}\). The 'moles' will cancel out and the answer will be in grams.

Key Concepts

Molar Mass

The concept of molar mass is pivotal when dealing with chemical quantities. It is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). Think of it as the 'atomic weight' for a compound, which takes into account the individual atomic masses of each element that composes it, as found in the periodic table.

Molar mass effectively bridges the gap between the micro (atoms, molecules) and the macro (grams) world, making it possible to convert from moles, a count of particles, to grams, which is a measure of mass we can practically sense. For instance, the molar mass of gold (Au) is 197 g/mol, meaning each mole of gold weighs 197 grams.

Stoichiometry

Stoichiometry is an essential topic in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. This field of study is not only about balancing equations but also about understanding the relationships and conversions between different substances involved in a reaction.

Through stoichiometry, the concept of the mole serves as a central unit, allowing chemists to work with amounts in the laboratory without having to count every atom or molecule. Stoichiometry leverages the laws of conservation of mass and fixed proportions to ensure chemical equations represent the science accurately.

To navigate stoichiometric calculations, you'll often convert moles of one substance to moles of another using the balanced chemical equation, and then use molar masses to convert moles into grams if needed.

Chemical Calculations

Chemical calculations encompass a wide array of mathematical techniques used in chemistry to relate the quantities of reactants and products in a chemical reaction. They are built upon stoichiometry and molar masses, allowing chemists to predict yields, determine reactant quantities, and more.

For any such calculation, understanding the role of the mole is crucial. It serves as a bridge between the atomic scale and the macroscopic world. In performing chemical calculations, the accuracy of molar masses and the careful balancing of equations are essential to achieve precise and reliable results.

In the conversion from moles to grams, the steps are straightforward: identify the molar mass, treat it as a conversion factor, and multiply it by the number of moles to get the mass. This process not only applies to pure substances but is also the backbone of calculations in reactions where multiple substances interact.