Problem 11 - Chemistry The Science in Context

Question

What is the molarity of a solution that contains 1.00 mmol of solute per milliliter of solution?

Step-by-Step Solution

Answer

Answer: The molarity of the solution is 1.00 mM.

Step 1: Recall the definition of molarity

Molarity (M) is defined as the number of moles of solute (n) per liter of solution (L). The formula for molarity is: M = n/L

Step 2: Convert the given amount from mmol to moles

We are given 1.00 mmol of solute per milliliter of solution. To convert this to moles, we need to multiply by 10^-3, since 1 mmol = 10^-3 mol. So: 1.00 mmol × 10^-3 = 10^-3 mol

Step 3: Convert the volume from milliliters to liters

We are given the amount of solute per milliliter of solution, but we need the amount per liter. There are 1000 mL in 1 L. So for 1 mL, we have: 1 mL × 1000 = 1000 mL = 1 L

Step 4: Calculate the molarity using the formula

Now we have the moles of solute (10^-3 mol) and the volume of solution (1 L). We can use the formula for molarity to find the answer: M = (10^-3 mol)/(1 L) M = 10^-3 mol/L

Step 5: Express the molarity in appropriate units

The molarity of the solution is 10^-3 mol/L, which is equivalent to 1.00 mM. So the molarity of the solution is: 1.00 mM

Key Concepts

Molarity Definition

Understanding molarity is crucial for grasping solution chemistry concepts. Molarity, often represented by the symbol 'M', is a measure of concentration that tells us how many moles of a solute are present in a liter of solution. The formal definition of molarity can be succinctly put as the number of moles of solute ((moles)) divided by the volume of the solution in liters ((L)): \[ M = \frac{n}{L} \].

This concentration measurement is particularly useful because it allows us to directly relate the volume of a solution to the amount of a substance it contains. One key point to remember is that molarity is temperature-dependent since it involves volume, which can expand or contract with temperature changes. When solving problems involving molarity, it's important to ensure the correct units are used. Since molarity calculations require moles per liter, any given quantities must be converted to these units before proceeding.

Mole Conversion

In chemistry, mole conversion is an essential skill that bridges the microscopic world of atoms and molecules with the macroscopic world we can measure. The mole ((mol)) is a fundamental unit in chemistry that quantifies the amount of a substance. One mole is defined as exactly 6.022 x 10^23 particles (Avogadro's number), which can be atoms, molecules, ions, or other entities.

Quite often, the amount of solute in a solution is not provided in moles but in millimoles (mmol), grams, or other units. Therefore, being able to convert to moles is a key step in many calculations. For instance, converting millimoles to moles involves a simple multiplication by the factor of 10^-3, since \( 1 mmol = 10^{-3} mol \). Certainty in mole conversions is necessary for accurate and meaningful molarity calculations, and it's often a two-step process: first, convert the mass of a substance to moles using the molar mass, and then use mole conversions for further calculations as needed.

Solution Concentration

Solution concentration is a general term for how much solute is dissolved in a given quantity of solvent. Concentration can be expressed in several ways including molarity, molality, normality, and parts per million, among others. Each of these measurements provides useful information depending on the context of the problem or the conditions of the experiment.

While molarity is one of the most common ways to express concentration, particularly when dealing with reactions in solution, it is important to understand the realm in which this measure operates. For example, molarity does not factor in temperature changes, which can be crucial for precise experimental work.

Dilution and Concentration Adjustments

In the laboratory setting, you may also be tasked with diluting or concentrating a solution, which directly changes its molarity. The relationship between the initial and final concentrations and volumes is given by the equation \( M_1V_1 = M_2V_2 \), where \( M_1 \) and \( M_2 \) are the molarities and \( V_1 \) and \( V_2 \) are the volumes of the solution before and after the dilution or concentration process. Understanding the various ways to express concentration allows students to adapt to different scientific scenarios and accurately carry out their chemical calculations.