Question

Challenge Vinegar is 5\(\%\) acetic acid by mass and has a density of 1.02 \(\mathrm{g} / \mathrm{mL}\) .What mass of acetic acid, in grams, is present in 185 \(\mathrm{mL}\) of vinegar?

Short answer

The mass of acetic acid present in 185 mL of vinegar is approximately 9.435 grams.

Step-by-step solution

Calculate the mass of 185 mL of vinegar

To find the mass of vinegar, we can use the following formula: Mass (m) = Volume (V) × Density (ρ) Given the density (ρ) as 1.02 g/mL, we can find the mass (m) by inputting the volume (V) of 185 mL: m = 185 mL × 1.02 g/mL

Calculate the mass of acetic acid in the vinegar

Now that we have the mass of the vinegar, we can find 5% of this mass to calculate the mass of acetic acid present in it: Mass of acetic acid = 0.05 × Mass of vinegar From Step 1, we have calculated the mass of vinegar: m = 185 mL × 1.02 g/mL ≈ 188.7 g Now, finding 5% of this mass (mass of acetic acid in the vinegar): Mass of acetic acid = 0.05 × 188.7 g ≈ 9.435 g So, there are approximately 9.435 grams of acetic acid present in 185 mL of vinegar.

Key concepts

Density Calculations

Understanding density is crucial when working with substances in chemistry. Density, symbolized by \rho, is defined as the mass per unit volume of a substance. It is usually expressed in units such as grams per cubic centimeters \(\mathrm{g/cm^3}\) or grams per milliliter \(\mathrm{g/mL}\). The basic formula to calculate the mass of a substance based on its density is:
\(\text{Mass} (m) = \text{Volume} (V) \times \text{Density} (\rho)\).

In the context of the given problem, the density of vinegar is provided, and a volume is specified. The initial step is simply to multiply these two values. This reveals the total mass of the vinegar, a foundational piece of information needed for further calculations.

Solution Concentration

Solution concentration often refers to the amount of solute present in a given amount of solution. There are various ways to measure concentration, but one common method is by mass percent. The mass percent of a component in a solution is calculated by taking the mass of that component and dividing it by the total mass of the solution, then multiplying by 100 to convert to a percentage.

Pertaining to our exercise, vinegar is a solution of acetic acid in water. The 5% mass percent tells us that 5 grams of acetic acid are present in every 100 grams of vinegar. To find the mass of acetic acid in a particular volume of vinegar, we first find the total mass of vinegar (from the density calculation), and then determine 5% of that mass. This simple yet effective approach allows us to clearly understand the concentration of acetic acid in vinegar and can be applied to any substance with similar given data.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. The unit for molar mass is grams per mole \(\mathrm{g/mol}\). It is a bridge between the mass of a substance and the number of moles since each mole represents Avogadro's number \(6.022\times10^{23}\) of particles, whether they are atoms, molecules, ions, or others.

To calculate the mass of a single molecule or atom, we can use the formula:
\(\text{Molar Mass} = \frac{\text{Mass of sample}}{\text{Number of moles}}\).
While molar mass isn't directly used in the provided exercise, it plays an important role in many chemical calculations, especially when converting between mass and moles in chemical equations or when dealing with stoichiometry. For example, if we needed to find the number of moles of acetic acid in the aforementioned 185 mL of vinegar, we would first find the mass of the acetic acid and then use its molar mass to find the number of moles.