Question

How many moles of carbon are there in a diamond weighing \(2.55 \mathrm{~g}\) ?

Short answer

There are approximately 0.212 moles of carbon in a diamond weighing 2.55 g.

Step-by-step solution

Determine the molar mass of carbon

First, you need to know the molar mass of carbon. The molar mass of carbon (C) is approximately 12.01 g/mol. This value can be found on the periodic table of elements.

Convert grams to moles

To find out how many moles of carbon are present in the diamond, use the formula: number of moles = mass / molar mass. Substitute the mass of the diamond (2.55 g) and the molar mass of carbon (12.01 g/mol) into the formula.

Calculate the number of moles of carbon

Using the formula from Step 2, you calculate the number of moles as follows: number of moles = 2.55 g / 12.01 g/mol, which equals approximately 0.212 moles.

Key concepts

Molar Mass

Understanding the concept of molar mass is crucial for various chemical calculations. The molar mass is defined as the mass of one mole of a substance, and it is measured in grams per mole (g/mol). Essentially, it reflects the weight of a collection of Avogadro's number (\(6.022\times10^{23}\) particles) of atoms or molecules. For elements, the molar mass is the atomic weight as listed on the periodic table.

To understand this in a practical context, consider the element carbon (C). Carbon has a molar mass of approximately 12.01 g/mol. This means that one mole of carbon atoms weighs about 12.01 grams. When dealing with a substance that is a single element like carbon in diamond form, the molar mass directly corresponds to the atomic weight of that element.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is a quantitative relationship based on the conservation of mass and the concept of moles. Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given reaction.

At the heart of stoichiometry lies the balanced chemical equation, which reflects the proportion of molecules and atoms involved. To manipulate and understand these ratios, knowledge of the molar masses of the substances involved is essential. Stoichiometry not only helps in calculating quantities but also enables the conversion between mass, moles, and the number of particles, bridging the gap between the macroscopic and atomic scales.

Periodic Table

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties. Elements are presented in order of increasing atomic number, and the table is structured to highlight periodic trends. One of the most important pieces of information that can be derived from the periodic table is the atomic weight of elements, which is essential for calculating molar masses.

For instance, when dealing with carbon, the periodic table indicates that its atomic weight and hence its molar mass is 12.01 g/mol. This understanding is foundational in conducting accurate calculations in chemistry. By referring to the periodic table, students and chemists can readily access the molar masses of elements required for stoichiometric calculations.

Conversion of Grams to Moles

The conversion of grams to moles is a basic skill in chemistry used to compare amounts of substances. To perform this conversion, one uses the formula: number of moles = mass (in grams) / molar mass (g/mol). This equation is fundamental for interpreting measurements in a chemical context, allowing the translation of laboratory scale weights into the mole scale, which is used for chemical equations and stoichiometry.

By understanding this conversion, students can solve problems that require knowing the amount of substance in moles, as illustrated by our example problem. Given a mass of 2.55 g for a diamond, which is composed solely of carbon, and knowing the molar mass of carbon is 12.01 g/mol, the formula facilitates the determination of the number of moles of carbon in the diamond. The application of this basic yet powerful concept is pervasive throughout chemical understanding and experimentation.