Problem 73 - Chemistry Matter and Change

Question

How many moles of BaS would be used to make \(1.5 \times 10^{3} \mathrm{mL}\) of a 10.0 \(\mathrm{M}\) solution?

Step-by-Step Solution

Answer

15.0 moles of BaS are used.

Step 1: Understand Molarity

Molarity is defined as the number of moles of solute per liter of solution. Given as 10.0 M for BaS, it means there are 10.0 moles of BaS in every 1 liter (or 1000 mL) of solution.

Step 2: Convert Milliliters to Liters

We need the volume in liters to use it in our molarity formula. Convert 1500 mL to liters by dividing by 1000: \[1500 \text{ mL} = \frac{1500}{1000} \text{ L} = 1.5 \text{ L}\]

Step 3: Use the Molarity Equation

The formula for molarity is: \[M = \frac{n}{V} \]where \(M\) is the molarity, \(n\) is the number of moles, and \(V\) is the volume in liters. We can rearrange this to find the number of moles:\[n = M \times V\]Substitute the given values for \(M\) and \(V\):\[n = 10.0 \times 1.5 = 15.0\]

Step 4: Calculate the Number of Moles

After performing the calculation in the previous step, we find that the number of moles of BaS required is 15.0 moles.

Key Concepts

Moles of Solute

Understanding the moles of solute is crucial in chemistry, especially when dealing with solutions. The term *moles* refers to the amount of substance. It is a fundamental unit in chemistry, representing a large number of molecules or atoms. To determine moles of a solute in a solution, you need to know two things: the molarity of the solution and the volume it occupies. A mole is a handy concept that allows scientists to count particles by weighing them. For instance, in the context of making a solution, you'll calculate how many moles of a solute like BaS are needed. In the exercise, knowing that the molarity is 10.0 M means that in every liter of solution, there are 10 moles of BaS. Using this understanding, you can easily calculate the total moles required for a given volume of solution.

Conversion from Milliliters to Liters

Many times, the volume of a solution is given in milliliters, especially in chemistry lab settings. However, molarity calculations always require the volume to be in liters. Thus, one must know how to convert milliliters to liters. This conversion process is quite simple:

• Remember that 1 liter equals 1000 milliliters.
• To convert milliliters to liters, divide the number of milliliters by 1000.

Applying this to our exercise example: 1500 mL is divided by 1000 to yield 1.5 liters. Converting accurately is essential, as an incorrect conversion can lead to wrong results in your calculations, impacting experiments or chemical reactions.

Molarity Equation

Understanding the molarity equation is essential to calculate how much of a solute is needed in a given solution. The molarity equation is represented as:\[ M = \frac{n}{V} \]Where:

• \(M\) is the molarity (moles per liter).
• \(n\) is the number of moles of solute.
• \(V\) is the volume of the solution in liters.

From this basic equation, you can rearrange the formula to solve for the number of moles needed:\[ n = M \times V \]In our exercise, substitute the given molarity of 10.0 for \(M\) and converted volume of 1.5 liters for \(V\). The result gives you the number of moles, which is 15.0 moles of BaS. This understanding of the molarity equation is vital, as it helps you compute how much solute you need for a specific concentration, ensuring that your experiments and solutions work as intended.