How many moles of sucrose are contained in each solution? (a) \(3.4 \mathrm{~L}\) of a \(0.100 \mathrm{M}\) sucrose solution (b) \(0.952 \mathrm{~L}\) of a \(1.88 \mathrm{M}\) sucrose solution (c) \(21.5 \mathrm{~mL}\) of a \(0.528 \mathrm{M}\) sucrose solution

In chemistry, understanding moles of solute is crucial. A mole is a unit that measures the amount of a substance. Specifically, one mole is equal to Avogadro's number (\(6.022 \times 10^{23}\) particles). When we talk about moles of solute, we're referring to the amount of solute, which is the substance dissolved in a solution.

In the given exercise, sucrose is the solute which needs to be measured. To determine how many moles of sucrose are present, one must know the volume of the solution along with its concentration in molarity. This can seem tricky, but once you grasp that you're basically counting the number of molecules in a given volume it becomes much simpler to understand. The idea that there can be a 'pile' of molecules in a certain space (like in one liter of solution) will help with visualizing what exactly a mole is.

Molarity, symbolized as M, is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution. The molarity formula is straightforward: \[\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\] or, when rearranged to find moles: \[\text{moles of solute} = \text{Molarity} \times \text{volume of solution in liters}\]

In the provided exercise, this formula is key to solving each part. It's simply a matter of plugging values into the formula. Ensure to always keep units consistent and to convert volumes to liters if they’re not already, as molarity is defined with respect to liters. An understanding of the molarity formula will enable students to grasp how to determine the amount of substance in a given volume, which is an essential skill in many areas of chemistry.

In the context of the problem, volume conversion is necessary to utilize the molarity formula correctly. Most commonly, you will need to convert milliliters to liters, since molarity is defined in terms of liters. The conversion is simple: to get from milliliters (mL) to liters (L), you divide by 1,000 since there are 1,000 milliliters in a liter.

For example, the exercise mentions a volume of 21.5 mL. To convert this to liters, you'll do the following calculation: \[21.5 \text{ mL} = \frac{21.5}{1000} \text{ L} = 0.0215 \text{ L}\] Once the conversion is done, this new volume in liters can be plugged into the molarity formula to find the moles of solute. Understanding this step is critical to ensure accurate calculations in chemistry.