Question

How many moles of \(\mathrm{HCl}\) are contained in \(100.0 \mathrm{~mL}\) of \(0.15 \mathrm{M} \mathrm{HCl}\) ?

Short answer

There are 0.015 moles of HCl in 100ml of a 0.15M HCl solution.

Step-by-step solution

Understand Molarity

Molarity (\(M\)) is defined as the number of moles of solute (\(n\)) divided by the volume of solution (\(V\)) in liters. Molarity = \( \frac{n}{V} \) By manipulating the formula, we can calculate the number of moles as:Number of moles, \(n\) = Molarity (\(M\)) * Volume (\(V\))

Convert the Volume from mL to Liters

Here, the volume is given in \( \mathrm{mL} \). However, the volume in the molarity formula must be in liters. There are 1000 \( \mathrm{mL} \) in a liter. So the volume in liters is: \(V\) (liters) = \( \frac{100.0}{1000} \) = 0.1 L.

Substitute values and calculate

By substituting the molarity and volume into the formula, we can now solve for n (number of moles):\(n\) = Molarity * Volume \(= 0.15M * 0.1L = 0.015 moles\)

Key concepts

Moles of Solute

Understanding the concept of moles is fundamental in chemistry. A mole is a unit that measures the amount of a substance. It helps chemists express quantities of the chemical compound involved in chemical reactions and solutions. The number of moles of a solute refers to how many units (or molecules) of that substance are present in a given sample. For instance, when we talk about a solution of hydrochloric acid (HCl), knowing the number of moles allows us to understand exactly how much HCl is dissolved in the solution. This becomes useful in various chemical calculations, such as when predicting the outcomes of chemical reactions or determining solution concentrations. In our problem, we wanted to calculate how many moles of HCl are present in 100.0 mL of a 0.15 M solution. Using the concept of moles, we can then apply the molarity formula to find our answer.

Conversion of Units

Accurate unit conversion is crucial in any scientific calculation because incorrect units can lead to incorrect solutions. In the context of molarity calculations, converting volume into the right units is essential. Molarity is typically expressed in terms of liters. However, in practical scenarios, volumes are often given in milliliters. Therefore, converting milliliters to liters is a necessary step in finding the correct molar concentration. Let's look at how this is done: there are 1000 milliliters in a liter. This means you divide the milliliters by 1000 to get the volume in liters. For example, if given 100.0 mL, converting this to liters is done as follows:

• Divide 100.0 by 1000.
• The result is 0.1 L.

This conversion ensures the volume is in the proper units, making the use of molarity straightforward with the appropriate values.

Molarity Formula

Molarity (M) is a common way to express concentration. It tells us how many moles of a solute are present in one liter of solution. The molarity formula is given by:\[ M = \frac{n}{V} \]where:

• \(n\) = number of moles of solute
• \(V\) = volume of solution in liters

To solve for the number of moles of solute (\(n\)), you multiply the molarity by the volume:\[ n = M \times V \]Applying this to the problem, if we know the molarity of the HCl solution is 0.15 M and the volume of the solution is 0.1 L, the number of moles can be calculated as:\[ n = 0.15 \times 0.1 = 0.015 \text{ moles} \]This step-by-step calculation demonstrates how to apply the formula to find out precisely how many moles of solute are present in a given volume of solution. The simplicity and usefulness of the molarity formula makes it a staple in chemistry for preparing solutions and understanding their concentrations.