Problem 78 - Chemistry The Molecular Science

Question

The density of a solution of sulfuric acid is \(1.285 \mathrm{~g} / \mathrm{cm}^{3}\), and it is \(38.08 \%\) acid by mass. Calculate the volume of solution (in \(\mathrm{mL}\) ) that contains \(125 \mathrm{~g}\) of sulfuric acid.

Step-by-Step Solution

Answer

The volume of the solution is approximately 255.32 mL.

Step 1: Determine the mass of the solution

The mass percentage tells us that for every 100 grams of solution, there are 38.08 grams of sulfuric acid. Using this, set up an equation to find the total mass of the solution that contains 125 grams of sulfuric acid. \[ 38.08 ext{ g } ext{ of acid} = rac{125 ext{ g } ext{ of acid}}{m_{ ext{solution}}} \] Solve for the total mass (\(m_{ ext{solution}}\)): \[ m_{ ext{solution}} = rac{125 ext{ g } imes 100}{38.08 ext{ g}} \approx 328.07 ext{ g} \] This is the total mass of the solution required.

Step 2: Calculate the volume of the solution

We have the total mass of the solution and the density is provided as 1.285 g/cm³. Use the formula \( ext{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the volume. Rearrange the formula to solve for volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{328.07 ext{ g}}{1.285 ext{ g/cm}^3} \approx 255.32 ext{ cm}^3 \] Since 1 cm³ is equivalent to 1 mL, the volume is the same in mL.

Key Concepts

Sulfuric Acid

Sulfuric acid, with the chemical formula \( \text{H}_2\text{SO}_4 \), is a highly corrosive substance used in various chemical processes. Its properties make it one of the most important industrial chemicals. At room temperature, it's a dense, oily liquid. Because of its high reactivity, sulfuric acid is utilized in producing fertilizers, manufacturing chemicals, refining oil, and many more applications.

If you are working with sulfuric acid in the laboratory or industry, it's crucial to handle it with care due to its corrosive nature. It reacts exothermically with water, which means it releases heat. Always add acid to water, not water to acid, to prevent violent reactions.

When calculating properties involving sulfuric acid, such as preparing a solution, knowing its concentrated nature will help in understanding density and mass percentage calculations.

Mass Percentage

Mass percentage is a way of expressing concentration, alluding to the proportion of a component in a mixture or solution relative to the total mass. Here, it is used to determine how much sulfuric acid is in a solution.

In our exercise, the sulfuric acid solution has a mass percentage of 38.08%, implying that in every 100 grams of the solution, 38.08 grams are sulfuric acid. This helps in understanding the concentration when calculating the mass of the solution required for certain tasks.

Calculating the mass of a solution based on mass percentage involves setting up a proportion. You solve for the total mass where you have the mass of one component and its percentage.

The formula is given by:

• \( \text{Mass of solution} = \frac{\text{Mass of component} \times 100}{\text{Mass percentage}} \)

This equation helps in solving for an unknown mass when the mass of one component and its concentration are known.

Solution Volume Calculation

When calculating the volume of a solution from its mass, density comes into play. Density is defined as mass per unit volume. It is used to relate how much space a substance occupies in relation to its mass.

In this exercise, the solution's density is given as 1.285 g/cm³. To find the volume, you use the rearranged density formula:

• \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \)

By this calculation, you input the total mass of the solution (328.07 g) to find its volume. Understanding this relationship helps in various chemical processes where knowing the amount of chemicals needed in a specific volume is crucial.

Since 1 cubic centimeter (cm³) is equivalent to 1 milliliter (mL), once you find the volume in cm³, it directly converts to mL, making it easy to measure the liquid solution.