Problem 20 - Chemistry: An Atoms-Focused Approach

Question

A sample of crude oil contains \(3.13 \mathrm{m} M\) naphthalene, \(12.0 \mathrm{mM}\) methylnaphthalene, \(23.8 \mathrm{mM}\) dimethylnaphthalene, and \(14.1 \mathrm{m} M\) trimethylnaphthalene. What is the total number of moles of all the naphthalene compounds in \(100.0 \mathrm{mL}\) of the oil?

Step-by-Step Solution

Answer

Answer: The total number of moles of all the naphthalene compounds in 100 mL of the crude oil is 0.005303 mol.

Step 1: Convert concentrations to moles

First, we need to convert the concentrations given in millimoles per liter (mM) to moles (M). Recall that 1 mM is equal to 0.001 M. So, we have the following: - Naphthalene: \(3.13 \mathrm{mM} = 3.13 \times 0.001 \ \mathrm{M} = 0.00313 \ \mathrm{M}\) - Methylnaphthalene: \(12.0 \mathrm{mM} = 12.0 \times 0.001 \ \mathrm{M} = 0.012 \ \mathrm{M}\) - Dimethylnaphthalene: \(23.8 \mathrm{mM} = 23.8 \times 0.001 \ \mathrm{M} = 0.0238 \ \mathrm{M}\) - Trimethylnaphthalene: \(14.1 \mathrm{mM} = 14.1 \times 0.001 \ \mathrm{M} = 0.0141 \ \mathrm{M}\)

Step 2: Calculate the number of moles in 100 mL of oil

Now, we'll calculate the number of moles of each compound in 100 mL of oil. Remember that the formula for calculating moles is: moles = concentration × volume (in liters) We'll do this calculation for each compound: - Naphthalene: \(0.00313 \ \mathrm{M} \times 0.100 \ \mathrm{L} = 0.000313 \ \mathrm{mol}\) - Methylnaphthalene: \(0.012 \ \mathrm{M} \times 0.100 \ \mathrm{L} = 0.0012 \ \mathrm{mol}\) - Dimethylnaphthalene: \(0.0238 \ \mathrm{M} \times 0.100 \ \mathrm{L} = 0.00238 \ \mathrm{mol}\) - Trimethylnaphthalene: \(0.0141 \ \mathrm{M} \times 0.100 \ \mathrm{L} = 0.00141 \ \mathrm{mol}\)

Step 3: Find the total number of moles

Finally, to find the total number of moles of all the naphthalene compounds in 100 mL of oil, we will add the moles calculated in step 2: Total moles = moles of naphthalene + moles of methylnaphthalene + moles of dimethylnaphthalene + moles of trimethylnaphthalene Total moles = (0.000313 + 0.0012 + 0.00238 + 0.00141) \(\ \mathrm{mol}\) Total moles = 0.005303 \(\ \mathrm{mol}\) Thus, the total number of moles of all the naphthalene compounds in 100 mL of the crude oil is 0.005303 mol.

Key Concepts

Molality

Molality is a measure of the concentration of a solution. It indicates the number of moles of solute per kilogram of solvent. This is particularly useful because it doesn't change with temperature, unlike molarity which is volume-based. To calculate molality, you need to know the mass of the solvent and the amount of solute in moles. The formula for molality is:\[Molality = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}.\]Why is this important?
- Molality helps in understanding interactions in reactions at microscopic levels.
- It remains constant under temperature variations, which is helpful in experiments involving heat.When given a solution's concentration in molality, you can determine how the solution will behave under different conditions without worrying about temperature affecting concentration measurements.

Solution Concentration

Solution concentration refers to the amount of solute that is dissolved in a solvent. Different units measure concentration, including molarity (M), molality (m), mole fraction, mass percent, etc. Within this problem, millimoles per liter (mM) are used to express concentration, which is a milli form of molarity. Understanding the basics:
- Concentration helps us express the proportion of species in a mixture.
- It's vital for standardized reactions, where precise reactant quantities are required.Important Calculations:
When converting mM to M, you multiply by 0.001 since 1 mM is equivalent to \(0.001\ M\). This unit conversion is essential because many calculations in chemistry require moles per liter (M). Solution concentration allows you to predict how reactions will perform, as reaction rates often depend on the concentration of reactants.

Chemistry Problem Solving

Problem solving in chemistry often requires a structured approach, using given data and converting them into useful forms. Understanding the problem statement, identifying known values, and converting units can be key steps to solving chemistry problems effectively. In this exercise, the step-by-step solution clearly shows how such an approach is implemented: Essential Steps for Problem Solving:
1. Identify what you are given and what you need to find.
2. Convert units so that they are in the correct form for calculation.
3. Apply relevant formulas to calculate desired values.
4. Sum up where appropriate to find totals or averages.

The approach in this problem involves converting concentrations from millimoles to moles and then calculating the total moles for all compounds. This demonstrates conversion and summation skills, which are crucial techniques in solving many chemistry questions successfully.

Crude Oil Composition

Crude oil composition is complex, containing hundreds of different hydrocarbon compounds. In this problem, we focus on naphthalene compounds, which are aromatic hydrocarbons found in oil. Understanding these compounds is important for refining processes, as they can affect the quality and characteristics of the fuel produced. Significant Points:
- Aromatic compounds like naphthalene have distinct properties, often used in dyes, plastics, and solvents.
- These compounds' presence in crude oil needs monitoring, as they influence the oil's overall quality and performance.

The ability to quantify the amount of each compound in crude oil helps in optimizing refining methods, ensuring efficient production of desired products while minimizing waste and environmental impact. This exercise illustrates the step-by-step methodology needed to quantify such compounds, which is pivotal in chemical process industries.