Problem 56 - Introductory Chemistry Atoms First

Question

Given some mass \(m\) of a known pure substance, what is the quickest way to determine the number of moles \(n\) you have of the substance?

Step-by-Step Solution

Answer

To determine the number of moles \(n\) of a given mass \(m\) of a known pure substance, follow these steps: (1) Identify the substance and its mass. (2) Determine the molar mass of the substance from the periodic table or a chemical data table. (3) Calculate the number of moles using the formula \(n = \frac{m}{\text{molar mass}}\), with mass in grams and molar mass in grams per mole (g/mol).

Step 1: Identify the substance and its mass

Determine the identity of the known pure substance and its given mass \(m\). This information should be provided in the problem.

Step 2: Determine the molar mass of the substance

Locate the substance on the periodic table or look in a chemical data table to find its molar mass. The molar mass has units of grams per mole (g/mol).

Step 3: Calculate the number of moles

Use the formula n = (mass of substance) / (molar mass of substance) to calculate the number of moles \(n\) of the substance. Make sure that the mass of the substance (\(m\)) is in grams and that the molar mass has units of grams per mole (g/mol) for the calculation to work properly. With these three steps, you can quickly determine the number of moles \(n\) of a given mass \(m\) of a known pure substance.

Key Concepts

Molar Mass

When determining the amount of a substance in chemistry, we often talk about moles. But to calculate these moles, the concept of "molar mass" is essential. Molar mass tells us how much one mole of a particular substance weighs. The molar mass is expressed in grams per mole (g/mol). To find the molar mass of a substance, you need to add up the atomic masses of all the atoms in a molecule of that substance. For instance, if you have water (H₂O), you would add the atomic masses of two hydrogen atoms and one oxygen atom.

• Determine atomic masses from the periodic table.
• Sum the atomic masses according to the number of each atom in the molecule.
• Express the total mass in g/mol.

Knowing the molar mass allows you to convert between the mass of a substance and the number of moles.

Pure Substance

A pure substance is crucial in chemistry problems as it refers to a material with a constant composition. Elements or compounds that are not mixed with any other substance qualify as pure. When you're given a problem regarding a pure substance, you can be certain of its exact chemical formula, making it easier to calculate its molar mass and, accordingly, the number of moles.

• No impurities exist in a pure substance.
• Pure substances have consistent and predictable properties.
• Common examples include pure elements like gold (Au) or compounds like water (H₂O).

Understanding the nature of a pure substance ensures accuracy in measurement and calculations for moles using molar mass.

Periodic Table

The periodic table is an essential tool in chemistry, acting as a map for all the elements. Chemists use it to find important information about each element, such as atomic number, symbol, and atomic mass. The atomic mass found on the periodic table is used to calculate the molar mass of substances, which, in turn, helps in determining moles.

• Atomic number indicates the number of protons in an atom.
• Atomic mass gives the average mass of the atoms of an element, crucial for calculating molar mass.
• The table is organized in groups and periods to reflect element properties and reactivity.

Knowing how to navigate this table is vital for finding the molar mass quickly and efficiently.

Grams per Mole

"Grams per mole" is a unit used to express molar mass in chemistry. It indicates how many grams there are in one mole of a substance. This unit is vital when converting between the mass of a substance and the amount in moles. For instance, if a substance has a molar mass of 44 g/mol, that means one mole of this substance weighs 44 grams.

• Makes conversion straightforward: mass in grams to moles, and vice versa.
• Helps in accurate and efficient experimentation and product formulation.
• Ensures standardized comparability between different substances.

This unit allows chemists to communicate in the same language, making calculations universal and understandable across different labs and studies.