Problem 76 - General Chemistry

Question

Insulin is a hormone that controls the use of glucose in the body. How many moles of insulin are required to make up \(28 \mathrm{~mL}\) of \(0.0048 \mathrm{M}\) insulin solution?

Step-by-Step Solution

Answer

0.0001344 moles of insulin are required.

Step 1: Understand the Formula for Molarity

The molarity (M) of a solution is defined as the number of moles of solute divided by the volume of the solution in liters. The formula is given by \( M = \frac{n}{V} \), where \( M \) is molarity, \( n \) is the number of moles, and \( V \) is the volume in liters.

Step 2: Convert Volume from mL to Liters

Since molarity is measured in moles per liter, we must convert the given volume from milliliters to liters. We know that 1 L = 1000 mL. Therefore, to convert 28 mL to liters, we use the conversion: \( 28\, \text{mL} \times \frac{1 \text{ L}}{1000\, \text{mL}} = 0.028 \) L.

Step 3: Rearrange Formula to Solve for Moles

Now that we have the volume in liters, use the formula \( M = \frac{n}{V} \) to find the number of moles \( n \). Rearranging gives \( n = M \times V \).

Step 4: Substitute Values and Calculate Moles

Substitute the known values into the formula: \( n = 0.0048 \text{ M} \times 0.028 \text{ L} = 0.0001344 \text{ moles} \). Calculate to find the number of moles of insulin required.

Key Concepts

Moles of Solute

When dealing with solutions, the concept of moles is fundamental. A mole is a standard unit of measurement in chemistry, which represents a very large number of molecules. Think of it like a "chemist's dozen," specifically Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles. In our problem, insulin is the solute—this is the substance that is being dissolved within a solution.
To figure out how many moles of a solute, like insulin, you would need, you can use the formula for molarity:

• \(M = \frac{n}{V}\)

where \(M\) is the molarity in moles per liter, \(n\) stands for the number of moles of insulin, and \(V\) is the volume of the solution in liters. This tells us that by rearranging the formula to \(n = M \times V\), we can solve for the number of moles, knowing the molarity and the volume.

Volume Conversion

Volume conversion is a crucial step when working with molarity. In most scientific calculations, the volume must be in liters rather than milliliters. This is because molarity is described in terms of liters, not milliliters. Getting the units right ensures that the final calculation will be correct.
To convert milliliters to liters, you use the fact that:

• 1 liter (L) = 1000 milliliters (mL)

Thus, when you have 28 mL to start, you convert it to liters by multiplying by \(\frac{1 \text{ L}}{1000 \text{ mL}}\). This gives \(0.028\) L. Remember, getting this conversion right is pivotal for plugging it into the formula correctly.

Insulin Solution Concentration

Concentration of a solution indicates how much solute is present in a given volume of solution. The molarity of the solution gives us this concentration, which in the case of insulin is \(0.0048\) M. This value shows that there are \(0.0048\) moles of insulin for every liter of solution.
To know how much insulin is needed for a specific volume of solution, you can rely on your previous calculations. By multiplying the molarity by the converted volume in liters, you calculate the number of moles needed. For example:

• \(n = 0.0048 \text{ M} \times 0.028 \text{ L} = 0.0001344 \text{ moles}\)

This simple multiplication gives you the exact amount of moles of insulin needed to make up the desired solution, highlighting the importance of precisely knowing both the concentration and volume.