Question

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

The mass of the solution in 1.00 L of soda is 1000 g, and the mass percentage of sodium benzoate is 0.5% or 0.005 in decimal form. The mass of sodium benzoate in the solution can be found using the formula: Mass of sodium benzoate = Mass percentage × Mass of solution = 0.005 × 1000 g = 5 g. Therefore, the approximate mass of sodium benzoate in 1.00 L of the solution is \(5 g\).

Step-by-step solution

Calculate the mass of the solution

Given that the density of soda is 1.00 g/mL and the volume is 1.00 L, we can find the mass of the solution using the formula: Mass = Density × Volume First, we need to convert the volume from Liters to milliliters: 1.00 L = 1000 mL Now, we can find the mass of the solution: Mass = (1.00 g/mL) × (1000 mL)

Calculate the mass of sodium benzoate in the solution

The mass percentage of sodium benzoate in the solution is 0.5%. Now, we will find the mass of sodium benzoate using the mass percentage and the mass of the solution. Use the formula: Mass of sodium benzoate = Mass percentage × Mass of solution Mass of sodium benzoate = 0.5% × Mass of solution First, convert the mass percentage to decimal form: 0.5% = 0.005 Now, substitute the mass of the solution calculated in step 1: Mass of sodium benzoate = 0.005 × (1.00 g/mL × 1000 mL)

Calculate the approximate mass of sodium benzoate

Now, calculate the mass of sodium benzoate: Mass of sodium benzoate = 0.005 × (1.00 g/mL × 1000 mL) = 0.005 × 1000 g = 5 g So, the approximate mass of sodium benzoate contained in 1.00 L of the solution is 5 g.

Key concepts

Density Calculation

Density is a fundamental concept that helps in determining the mass of a solution when you know its volume. It is expressed as mass per unit volume (in grams per milliliter for liquids).
To calculate the mass of the solution in the soda example, we use the formula:
Mass = Density × Volume.
Since the density of the soda is provided as 1.00 g/mL and the volume is given as 1.00 L (which converts to 1000 mL), we can directly apply the formula:

• Mass = (1.00 g/mL) × (1000 mL).
• The result is 1000 g.

This calculation tells us the total mass of the soda solution, an essential step as it serves as the basis for calculating the amount of sodium benzoate in later steps.

Solution Concentration

Solution concentration often refers to the amount of a substance (solute) present in a certain amount of solution. Here, it is expressed as a mass percent.
The mass percent is calculated as the mass of the solute divided by the total mass of the solution, then multiplied by 100. In our scenario, we know the soda contains 0.5% sodium benzoate.
To figure out the mass, we need to convert this percentage into a decimal as follows:

• 0.5% becomes 0.005 when expressed in decimal form.
• We then multiply by the mass of the solution (1000 g) previously calculated.

This gives us the formula:
Mass of sodium benzoate = 0.005 × 1000 g, resulting in 5 g.
Understanding concentration is crucial as it indicates how much solute is mixed with the solvent in the solution.

Mass Conversion

Mass conversion is the process of consistently transforming measurements to ensure calculations are straightforward and accurate. In this example, one must first convert the volume unit, since density is given in grams per milliliter, not per liter.

• Start by converting the volume given in liters to milliliters (1 L = 1000 mL), which aligns with the units of density.
• This process allows for the calculation of mass using the density-mass-volume relationship effectively.

Converting weights and measures ensures that all parts of your calculations speak the same mathematical language, facilitating precise and error-free results in your work. It ensures that every part of the equation complements the others, leading to a clear and correct final answer.