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Chapter 4: Problem 90

The soda you are drinking contains \(0.5 \%\) by mass sodium benzoate as a preservative. What approximate mass of sodium benzoate is contained in \(1.00 \mathrm{~L}\) of the solution assuming that the density of the soda is \(1.00 \mathrm{~g} / \mathrm{mL}\) (the approximate density of water)?

Short Answer

Expert verified
The approximate mass of sodium benzoate in 1.00 L of the soda solution is 5 g.

Step by step solution

01

Convert volume to milliliters

We are given 1.00 L of the solution. To convert this to milliliters, we use the conversion factor: \(1\mathrm{~L} = 1000\mathrm{~mL}\). So, we have: \(1.00\mathrm{~L} \times \dfrac{1000\mathrm{~mL}}{1\mathrm{~L}} = 1000\mathrm{~mL}\)
02

Determine the mass of the solution

The density of the soda is given as \(1.00 \mathrm{~g/mL}\). To find the mass of the solution, we use the formula: \(\text{mass} = \text{density} \times \text{volume}\) So, the mass of the solution is: \(\text{mass} = 1.00 \mathrm{~g/mL} \times 1000\mathrm{~mL} = 1000\mathrm{~g}\)
03

Calculate the mass of sodium benzoate

We are given that the mass percent of sodium benzoate in the soda is 0.5%. This means that for every 100 g of the solution, there are 0.5 g of sodium benzoate. We have 1000 g of the solution, so we can set up a proportion to find the mass of sodium benzoate, using the cross-multiplication technique: \(\dfrac{\text{mass of sodium benzoate}}{1000\mathrm{~g}} = \dfrac{0.5\mathrm{~g}}{100\mathrm{~g}}\) Now, solve for the mass of sodium benzoate: \(\text{mass of sodium benzoate} = \dfrac{0.5\mathrm{~g} \times 1000\mathrm{~g}}{100\mathrm{~g}} = 5\mathrm{~g}\) The approximate mass of sodium benzoate in 1.00 L of the solution is 5 g.

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