Problem 85 - Chemistry: Principles and Reactions

Question

Some brands of salami contain \(0.090 \%\) sodium benzoate \(\left(\mathrm{NaC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) by mass as a preservative. If you eat \(6.00 \mathrm{oz}\) of this salami, how many atoms of sodium will you consume, assuming salami contains no other source of that element?

Step-by-Step Solution

Answer

Answer: Approximately 6.39 × 10^{20} sodium atoms.

Step 1: Find the mass of sodium benzoate consumed

First, we need to find out how much sodium benzoate is present in the given amount of salami. To do this, we will multiply the percentage of sodium benzoate in the salami by the consumed mass. Given: Percentage of sodium benzoate in salami = \(0.090 \%\) Amount of salami consumed = \(6.00 \ oz\) First, we need to convert ounces to grams, as SI units are used in calculations. 1 ounce = 28.35 grams 6 oz × 28.35 g/oz ≈ 170.1 g Now we can find the mass of sodium benzoate consumed: Mass of sodium benzoate = (0.090/100) × 170.1 g ≈ 0.15309 g

Step 2: Calculate the moles of sodium benzoate consumed

In order to find the moles of sodium benzoate, we need to divide the mass of consumed sodium benzoate by its molar mass. Molar mass of sodium benzoate (\(\mathrm{NaC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\)) = 22.99 g/mol (Na) + 12.01 g/mol × 7 (C) + 1.01 g/mol × 5 (H) + 16.00 g/mol × 2 (O) ≈ 144.11 g/mol Moles of sodium benzoate = (Mass of sodium benzoate) / (Molar mass of sodium benzoate) Moles of sodium benzoate ≈ 0.15309 g / 144.11 g/mol ≈ 0.001062 mol

Step 3: Determine the moles of sodium atoms in the consumed sodium benzoate

In one mole of sodium benzoate, there is one mole of sodium atoms. Therefore, the moles of sodium atoms in the consumed sodium benzoate are equal to the moles of sodium benzoate consumed. Moles of sodium atoms = Moles of sodium benzoate ≈ 0.001062 mol

Step 4: Convert the moles of sodium atoms to the number of sodium atoms

Finally, we can use Avogadro's number to convert the moles of sodium atoms to the number of sodium atoms. Avogadro's Number, \(N_{A} = 6.022 \times 10^{23}\) atoms/mol Number of sodium atoms = Moles of sodium atoms × Avogadro's Number Number of sodium atoms ≈ 0.001062 mol × (6.022 × 10^{23} atoms/mol) ≈ 6.39 × 10^{20} atoms So, if you eat 6.00 ounces of this salami, you will consume approximately 6.39 × 10^{20} sodium atoms.

Key Concepts

Chemical Calculations

Chemical calculations are a fundamental part of chemistry, allowing us to predict amounts of reactants or products in a given reaction. In this problem, chemical calculations help us determine the mass of sodium benzoate in a specific amount of salami. We start by finding the percentage of sodium benzoate in salami (0.090%) and use it to calculate the exact mass present when consuming 6 ounces of salami, ultimately converting units to work in grams since scientific calculations often use SI units.

• First, the salami's weight in ounces is converted to grams. This ensures that subsequent calculations regarding concentration and mass are consistent.
• By determining how much sodium benzoate is present in those grams of salami, we see practical application of percentages, highlighting how a seemingly small concentration can significantly impact calculations.

These steps are the backbone of any chemical analysis and showcase fundamental skills needed for more complex calculations.

Molar Mass

Molar mass is the mass of one mole of a compound. It helps chemists convert between mass and moles, crucial for determining the number of molecules. In this problem, we calculate the molar mass of sodium benzoate (\(\mathrm{NaC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\)), a common preservative.
Calculating the molar mass involves summing the atomic masses of all atoms in a molecule. For sodium benzoate:

• Sodium (Na): 22.99 g/mol
• Carbon (C): 12.01 g/mol, multiplied by 7
• Hydrogen (H): 1.01 g/mol, multiplied by 5
• Oxygen (O): 16.00 g/mol, multiplied by 2

Adding these gives a molar mass around 144.11 g/mol. Understanding molar mass is essential for converting grams to moles, as gram measurements need to be expressed in the more manageable concept of moles for reactions.

Avogadro's Number

Avogadro's number is a key concept in chemistry, defined as the number of units (atoms, molecules) in one mole of a given substance. Here, it helps us convert moles of sodium to the number of atoms.
Avogadro's number (\(N_A\)) is approximately \(6.022 \times 10^{23}\) atoms/mol. With this constant:

• We can translate a mole-based measurement (such as moles of sodium atoms) into an actual count of atoms, useful for understanding reactions on both a macroscopic and molecular level.
• By multiplying the moles of sodium we calculated by Avogadro's number, we determine the immense quantity of atoms you consume — illustrating the concept that even small amounts of a compound involve enormous numbers of atoms.

This conversion helps illustrate the fundamental, vast scale at which chemical reactions and compositions occur.

Conversion of Units

Converting units is a daily practice in chemistry and is fundamental to solving real-world problems. Here, understanding conversions was crucial for transitioning from ounces to grams, ensuring the correct use of SI units in calculations.

• In this problem, converting 6 ounces of salami into grams (\(6 \text{ oz} \times 28.35 \text{ g/oz} = 170.1 \text{ g}\)) was essential before any other calculation could proceed.
• Appropriate unit conversion is also vital when determining the percentage mass (as percentages need consistent base units), ensuring that all subsequent calculations derive from a common measurement.

Proficiency in conversion helps prevent errors and ensures accuracy, fundamental to both laboratory work and in understanding complex chemical processes.