Problem 68 - General Chemistry

Question

A \(50.0-\mathrm{mL}\) volume of \(\mathrm{AgNO}_{3}\) solution contains \(0.0285\) mol \(\mathrm{AgNO}_{3}\) (silver nitrate). What is the molarity of the solution?

Step-by-Step Solution

Answer

The molarity of the solution is 0.570 mol/L.

Step 1: Understanding Molarity

Molarity is defined as the number of moles of solute (in this case, silver nitrate, \(\text{AgNO}_3\)) per liter of solution. The formula to find molarity (\(M\)) is given by \(M = \frac{n}{V}\), where \(n\) is the number of moles of solute and \(V\) is the volume of solution in liters.

Step 2: Convert Volume to Liters

The volume of the solution is given in milliliters, so we need to convert it to liters as molarity is expressed in terms of liters. There are 1000 milliliters in a liter, so: \(50.0\, \text{mL} = \frac{50.0}{1000}\, \text{L} = 0.0500\, \text{L}\).

Step 3: Calculate Molarity

Using the molarity formula \(M = \frac{n}{V}\), where \(n = 0.0285\, \text{mol}\) and \(V = 0.0500\, \text{L}\), we can substitute these values to find the molarity:\[ M = \frac{0.0285}{0.0500} = 0.570\, \text{mol/L} \]

Key Concepts

Mole Calculations

Mole calculations are a fundamental part of chemistry that focuses on determining the amount of substance present in a reaction or solution. The mole is a unit that quantifies the number of chemical entities, like atoms, ions, or molecules, in a substance. This unit is based on Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole.

To perform mole calculations effectively, you need to understand and use molar mass, which is the mass of one mole of a given element or compound measured in grams per mole. For instance, if you are given a certain mass of a compound, you can convert it to moles by dividing the mass by the compound's molar mass.

Whether you're calculating amounts in a reaction or determining concentrations in a solution, keeping track of moles is crucial. In our example, knowing there are \(0.0285\) moles of \(\mathrm{AgNO}_3\) helps establish how concentrated our solution is, allowing us to calculate its molarity.

Volume Conversion

Volume conversion is an essential skill in chemistry, especially when you're dealing with solutions and their concentrations. In solution chemistry, volumes are often given in milliliters, but calculations, like those for molarity, require the volume to be in liters. This is because molarity is expressed in terms of moles per liter.

To convert milliliters to liters, you divide the number of milliliters by 1000, since there are 1000 milliliters in one liter. This conversion factor is key every time you see a volume in milliliters in the context of calculating molarity or any other concentration-related measurement.

In the given example, we had to convert \(50.0\) milliliters of \(\mathrm{AgNO}_3\) solution into liters. By dividing 50 by 1000, we obtained a volume of \(0.0500\) liters. Such conversions ensure that all parts of concentration equations have compatible units, making the calculations accurate and straightforward.

Solution Concentration

Solution concentration describes how much solute is dissolved in a given amount of solvent or solution. Molarity is a common way to express concentration, defined as the moles of solute per liter of solution. This makes it an essential parameter for reactions and solutions in chemistry.

To calculate molarity, you use the formula \( M = \frac{n}{V} \), where \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. It’s imperative to ensure the volume is in liters to apply this formula correctly.

In our scenario, we know the number of moles of \(\mathrm{AgNO}_3\) (0.0285 mol) and its volume in liters (0.0500 L). By inserting these values into the formula, we calculate the molarity as \(0.570\, \mathrm{mol/L}\). Knowing the molarity of a solution is crucial as it helps predict how the solution will behave in chemical reactions, affecting reaction rates, equilibrium, and overall chemical behavior.