Problem 94 - Chemistry Matter and Change

Question

Perform the following conversions. a. \(1.51 \times 10^{15}\) atoms of Si to mol of Si b. \(4.25 \times 10^{-2}\) mol of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) c. \(8.95 \times 10^{25}\) molecules of \(\mathrm{CCl}_{4}\) to mol of \(\mathrm{CCl}_{4}\) d. 5.90 \(\mathrm{mol}\) of Ca to atoms of Ca

Step-by-Step Solution

Answer

The short version of the answer is: a. 2.51 x 10^(-9) moles Si b. 2.56 × 10^(22) molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) c. 1.49 × 10^2 moles \(\mathrm{CCl}_{4}\) d. 3.55 × 10^(24) atoms of Ca

Step 1: Write down the conversion factor

For 1 mole of Si, there are 6.022 x 10^23 atoms of Si. Here, our conversion factor is Avogadro's number: 1 mole Si = 6.022 x 10^23 atoms Si

Step 2: Conversion

To convert 1.51 × 10^15 atoms of Si to mol of Si, we can set up our calculation: Moles of Si = (1.51 × 10^15 atoms Si) x (1 mol Si / 6.022 × 10^23 atoms Si) Moles of Si = \( \dfrac{1.51 × 10^{15}}{6.022 × 10^{23}} \) moles Si Moles of Si = 2.51 x 10^(-9) moles Si b. 4.25 × 10^(-2) mol of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Step 1: Write down the conversion factor

The same conversion factor as in (a) can be used: 1 mol of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) = 6.022 × 10^23 molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Step 2: Conversion

Convert 4.25 × 10^(-2) mol of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to molecules: Number of molecules = (4.25 × 10^(-2) mol) x (6.022 × 10^23 molecules/mol) Number of molecules = 2.56 × 10^(22) molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) c. 8.95 × 10^25 molecules of \(\mathrm{CCl}_{4}\) to mol of \(\mathrm{CCl}_{4}\)

Step 1: Write down the conversion factor

This is the same conversion factor as in (a): 1 mole \(\mathrm{CCl}_{4}\) = 6.022 × 10^23 molecules \(\mathrm{CCl}_{4}\)

Step 2: Conversion

Convert 8.95 × 10^25 molecules of \(\mathrm{CCl}_{4}\) to mol of \(\mathrm{CCl}_{4}\): Moles of \(\mathrm{CCl}_{4}\) = (8.95 × 10^25 molecules) x (1 mol / 6.022 × 10^23 molecules) Moles of \(\mathrm{CCl}_{4}\) = \( \dfrac{8.95 × 10^{25}}{6.022 × 10^{23}} \) moles \(\mathrm{CCl}_{4}\) Moles of \(\mathrm{CCl}_{4}\) = 1.49 × 10^2 moles \(\mathrm{CCl}_{4}\) d. 5.90 mol of Ca to atoms of Ca

Step 1: Write down the conversion factor

The conversion factor is the same as in (a): 1 mol of Ca = 6.022 x 10^23 atoms of Ca

Step 2: Conversion

Convert 5.90 mol of Ca to atoms of Ca: Number of atoms = (5.90 mol Ca) x (6.022 × 10^23 atoms/mol) Number of atoms = 3.55 × 10^(24) atoms of Ca

Key Concepts

Avogadro's Number

Avogadro's Number is a key concept in chemistry that bridges the gap between atoms and moles. It represents the number of atoms, ions, or molecules contained in one mole of a substance, and its value is a hefty 6.022 x 10^{23}. This number is crucial because it allows chemists to convert between the atomic scale and amounts that can be physically measured in the laboratory. For instance, if you know how many atoms you have, you can easily convert them to moles using Avogadro's Number.

• Avogadro's Number simplifies conversions: Imagine counting over a sextillion atoms! Using moles is much more practical.
• It's used to quantify the number of entities in macroscopic amounts of a chemical sample, making it consistent with observable measurements.

Understanding this number helps in numerous calculations like determining the amount of reactants or products in a chemical reaction.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. Using stoichiometry, scientists can predict how much of a substance is needed or produced. It relies heavily on balanced chemical equations to do this.
A balanced chemical equation indicates the exact proportions, or stoichiometric coefficients, of reactants and products involved in the reaction. For example, in a simple reaction like \[2H_2 + O_2 \rightarrow 2H2O\]The coefficients indicate that two moles of hydrogen gas react with one mole of oxygen gas to yield two moles of water.

• Stoichiometry is like a recipe, it tells you how much of each ingredient you need.
• It helps in planning out chemical reactions to avoid wastage of reactants.

Mastering stoichiometry is essential for making accurate predictions and efficient use of resources in chemical processes.

Chemical Conversions

Chemical conversions are the backbone of chemistry calculations. They involve changing quantities between different units, typically using moles as the pivot point due to their relevance in the mole concept. For instance, converting atoms to moles or finding molecules from moles of a substance requires understanding both Avogadro's Number and the principles of stoichiometry.
Converting between different chemical units involves steps like:

• Identifying what's given and what needs to be found (e.g., atoms to moles, moles to molecules).
• Applying the appropriate conversion factor, such as Avogadro's Number, to carry out the conversion.

An example of this is converting atoms of silicon to moles of silicon. You use the conversion factor provided by Avogadro's Number:\[\text{Moles of Si} = \dfrac{1.51 \times 10^{15} \text{ atoms Si}}{6.022 \times 10^{23} \text{ atoms/mol}}\]This results in a minuscule amount, since we're dealing with an immense number of atoms packed into what is measured in the lab as moles.
Chemical conversions are foundational for anyone studying chemistry, allowing for precise formulation and interpretation of chemical data in practical and theoretical work.