Question

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

Short answer

Answer: Approximately 6.391 × 10^20 sodium atoms.

Step-by-step solution

Conversion of units

We have the amount of salami in ounces, but we need the mass in grams to perform calculations. Convert 6.00 oz to grams using the conversion factor (1 oz = 28.35 g): (6.00 oz) × (28.35 g/1 oz) = 170.10 g

Calculate the amount of sodium benzoate in salami

Calculate the mass of sodium benzoate (NaC7H5O2) present in 170.10 g of salami using the given percentage (0.090%): (170.10 g) × (0.090/100) = 0.15309 g of sodium benzoate

Calculate moles of sodium benzoate

Convert the mass of sodium benzoate to moles using its molar mass (Na = 22.99 g/mol, C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol): Molar Mass of sodium benzoate(NaC7H5O2) = 1(22.99) + 7(12.01) + 5(1.008) + 2(16.00) = 144.103 g/mol Number of moles = (0.15309 g) / (144.103 g/mol) = 0.00106158 mol

Calculate the number of sodium atoms

Use Avogadro's number (6.022 × 10^23 atoms/mol) to find the number of sodium atoms in the given moles of sodium benzoate: Number of sodium atoms = (0.00106158 mol) × (6.022 × 10^23 atoms/mol) = 6.391 × 10^20 sodium atoms Hence, there are about 6.391 × 10^20 sodium atoms consumed after eating 6.00 oz of salami containing 0.090% sodium benzoate as a preservative.