Problem 2 - Chemistry Matter and Change

Question

Calculate the number of molecules in 11.5 mol of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\)

Step-by-Step Solution

Answer

The number of molecules in 11.5 mol of water (H₂O) is approximately 6.93 x 10²⁴ particles.

Step 1: Write down the given information and the formula to use

We are given: - 11.5 mol of water (H₂O) - Avogadro's number: 6.022 x 10²³ particles/mol Formula to use: Number of molecules = (Amount in moles) x (Avogadro's number)

Step 2: Substitute the given values into the formula

Replace the amount in moles and Avogadro's number in the formula: Number of molecules = (11.5 mol) x (6.022 x 10²³ particles/mol)

Step 3: Calculate the number of molecules

Multiply the amount in moles by Avogadro's number to find the number of molecules: Number of molecules = (11.5 mol) x (6.022 x 10²³ particles/mol) ≈ 6.93 x 10²⁴ particles So, there are approximately 6.93 x 10²⁴ molecules in 11.5 mol of water (H₂O).

Key Concepts

Mole Concept

The mole concept is a core principle in chemistry that provides a simple way to quantify the amount of substance. One mole contains exactly 6.022 x 10²³ entities, typically atoms or molecules. This special number is known as Avogadro's number, named after the Italian scientist Amedeo Avogadro. The importance of the mole concept cannot be overstated. It acts as a bridge between the micro world of atoms and molecules and the macro world that we can measure and observe. When chemists speak of a mole of water, they are referring to 6.022 x 10²³ molecules of water. Why is the mole concept useful? Imagine counting each atom or molecule within a substance; it would be incredibly time-consuming. The mole gives scientists a practical means to count and compare different substances based on mass.

Calculating Molecules

Calculating the number of molecules in a substance requires understanding Avogadro's number. Start by knowing the amount of substance you have in moles because this is crucial to the calculation. When you want to calculate the total number of molecules in a given amount of moles of a substance, use this formula:

• Number of molecules = (Amount in moles) × (Avogadro's number)

For example, if you have 11.5 moles of water, you simply multiply the number of moles by Avogadro's number (6.022 x 10²³). Therefore, the calculation would look like this:

• (11.5 mol) × (6.022 x 10²³ molecules/mol) = approximately 6.93 x 10²⁴ molecules

This shows the powerfulness of Avogadro's number in transforming moles into actual physical numbers we can understand.

Chemical Calculations

Chemical calculations are essential when predicting the outcomes of chemical reactions and understanding proportions. For accurate chemical calculations, especially when dealing with molecules and atoms, using the mole and Avogadro's number is fundamental. Here's why chemical calculations matter:

• They help determine the amount of reactants needed for a reaction to occur.
• They predict the yield of a product in a given chemical reaction.
• They assist in optimizing commercial chemical production processes.

The exercise of calculating the number of molecules in 11.5 moles of water is a practical illustration of these principles. By converting moles to molecules, one ensures that the right quantities of materials are used, saving time and resources in practical applications. Applying these calculations in lab settings helps chemists make precise measurements, manufacture products, and innovate new substances, underpinning the technological progress in fields like pharmaceuticals and materials science.