Question

A solution is labeled \(0.25 M\) HCl. Construct two conversion factors that relate moles of \(\mathrm{HCl}\) to the volume of solution expressed in liters.

Short answer

The conversion factors are \( \dfrac{1 L}{0.25 moles} \) and \( \dfrac{0.25 moles}{1 L} \).

Step-by-step solution

Understand the Molarity Concept

The molarity (M) of a solution is defined as the number of moles of solute (HCl in this case) per liter of solution. Here, a solution with molarity of 0.25 M HCl means it contains 0.25 moles of HCl per liter of solution.

First Conversion Factor: Moles to Liters

To convert from moles of HCl to liters of solution, use the molarity. Since 0.25 M means 0.25 moles per liter, the first conversion factor is \( \dfrac{1 L}{0.25 moles} \). This can be used to find the volume when the number of moles is known.

Second Conversion Factor: Liters to Moles

To convert from liters of solution to moles of HCl, invert the molarity. The second conversion factor is \( \dfrac{0.25 moles}{1 L} \). This can be used to find the number of moles when the volume is known.

Key concepts

Conversion Factors

Conversion factors are vital tools in chemistry that allow us to relate different units of measurement to each other. These factors are ratios that express how much of one unit is equivalent to another unit. For example, consider a solution with a certain molarity. Here, molarity essentially serves as a conversion factor, allowing us to move between the volume of the solution and the moles of solute it contains.

When we talk about the conversion factors involving a 0.25 M HCl solution, these factors enable us to convert between the unit of moles (how much substance we have) and liters (how much space it occupies). The key to using conversion factors correctly is understanding the relationship between the units being converted and setting up the ratio so that the desired unit is isolated on one side of the equation. This will ensure that when you multiply by the conversion factor, units you want to cancel out will do so, leaving you with the correct units for your answer.

Moles of Solute

The concept of moles of solute is crucial for understanding the composition of a solution at the molecular level. A mole is a standard unit in chemistry that represents a specific quantity (Avogadro's number, or approximately 6.022 × 10²³) of atoms, molecules, or ions. When we talk about the moles of solute, we are referring to the amount of the dissolved substance within a given volume of solution.

The molarity (M) of a solution, which is moles of solute per liter of solution, gives us a direct method to quantify the concentration. In the case of our 0.25 M HCl solution, we know that there are 0.25 moles of HCl for every liter of solution. Understanding this relationship is fundamental for predicting how that solution will behave in different chemical reactions or when diluted.

Volume of Solution

The volume of the solution is another fundamental concept in chemistry, especially when working with solutions of known concentration. It refers to the space that the solution occupies and is usually measured in liters. Knowing the volume is essential when preparing solutions of a desired concentration or when performing dilutions.

In practice, to measure or calculate the volume of a solution, you can use the molarity and the conversion factors, just as discussed previously. With the 0.25 M HCl example, if a scientist has a specific amount of moles of HCl and needs to know the corresponding volume of solution, they can use the conversion factor \( \dfrac{1 L}{0.25 moles} \) to determine the volume in liters. Conversely, if they need to know how many moles are in a certain volume of that solution, they can use the inverse conversion factor \( \dfrac{0.25 moles}{1 L} \) to find this value. This interchangeability of moles and volume via molarity is indispensable in many chemistry calculations.