Problem 63 - Chemistry: An Atoms-Focused Approach

Question

A chemist needs \(35.0 \mathrm{g}\) of concentrated sulfuric acid for an experiment. The density of concentrated sulfuric acid at room temperature is \(1.84 \mathrm{g} / \mathrm{mL}\). What volume of the acid is required?

Step-by-Step Solution

Answer

Answer: The chemist needs to use 19.0 mL of concentrated sulfuric acid for the experiment.

Step 1: Write down the given values and equation

We need to find the volume of concentrated sulfuric acid (V). We are given the following information: - Mass (m) = 35.0 g - Density (D) = 1.84 g/mL We will use the equation, Volume (V) = Mass (m) / Density (D).

Step 2: Substitute the given values and solve for the volume

Using the given values and the equation, we can now find the volume: V = m / D Substitute the given values into the equation: V = (35.0\,\text{g}) / (1.84\,\text{g/mL}) Now, perform the calculation: V = 35.0 / 1.84 ≈ 19.0\,\text{mL}

Step 3: Write the final answer

The chemist needs to use 19.0 mL of concentrated sulfuric acid for the experiment.

Key Concepts

Density Calculation

Density is a crucial concept in chemistry that connects mass and volume. It's defined as mass per unit volume and is often expressed in grams per milliliter (g/mL) or kilograms per liter (kg/L). By using density, you can determine how much space a given mass of a substance occupies. This is particularly helpful when working with liquids and gases in chemistry.
To perform a density calculation, you need two main components:

• Mass (often given in grams or kilograms)
• Density (provided in units like g/mL or kg/L)

You'll often see the formula for density calculations written as follows:\[D = \frac{m}{V}\]Where \(D\) is the density, \(m\) is the mass, and \(V\) is the volume.
By rearranging this formula, you can solve for volume if you know the mass and density:\[V = \frac{m}{D}\]This manipulation forms the basis for many problems involving the measurement of substances, making density a fundamental concept to understand in chemistry.

Sulfuric Acid

Sulfuric acid is a strong mineral acid with the chemical formula \(H_2SO_4\). It is a widely used chemical in laboratories and industries due to its strong acidic nature and versatility. Here's what you need to know about sulfuric acid:

• It's highly corrosive and can cause burns; safety precautions are crucial when handling it.
• Sulfuric acid is often colorless and odorless, but it can appear yellow depending on its level of impurities.
• It dissolves in water exothermically, which means it releases heat when mixed with water, so always add acid to water, not the other way around.
• It's used in the production of fertilizers, petroleum refining, and chemical synthesis.

In a lab setting, concentrated sulfuric acid typically has a high density, like the 1.84 g/mL mentioned in our exercise. This indicates a substantial amount of mass packed into a smaller volume, which is characteristic of solutions with high dissolved solute quantities.

Volume Calculation

Volume calculations are essential in chemistry, especially when preparing solutions or reacting specific quantities of substances. The volume tells us how much space a substance occupies and is usually measured in liters or milliliters for liquids.
To calculate the volume, you can use the following formula, derived from the density equation:\[V = \frac{m}{D}\]Here's a breakdown of what each symbol represents:

• \(V\) stands for volume, measured in milliliters (mL) or liters (L).
• \(m\) is the mass of the substance, given in grams (g).
• \(D\) represents the density, provided in grams per milliliter (g/mL) or equivalent units.

By substituting your known values into this equation, you can find the desired volume. For instance, in our practice problem, we need to determine how much space 35.0 g of sulfuric acid occupies. Using the density 1.84 g/mL, we substitute and solve:\[V = \frac{35.0\, \text{g}}{1.84\, \text{g/mL}} \approx 19.0\, \text{mL}\]This calculated volume enables the chemist to precisely measure the amount of acid necessary for an experiment, ensuring accuracy and safety in chemical processes.