Question

How many moles of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), are contained in \(50.0 \mathrm{~g}\) of a \(0.85 \mathrm{~m}\) sucrose solution?

Short answer

The solution contains \(0.0425\) moles of sucrose.

Step-by-step solution

Convert grams to litres

With a water density of approximately 1 g/ml or 1 g/cm^3, convert 50 g to volume in litres. This gives the solution volume as \( \frac{50 g}{1 g/mL} = 50 mL \) or \( \frac{50 mL}{1000 mL/L} = 0.05 L \).

Use the molarity formula

Molarity (M) is a measure of the concentration of a solute in a solution, or of any chemical species in terms of volume. By definition, molarity = moles of solute/volume of solution in litres. We have a molarity of 0.85 mol/L, and a volume of 0.05 L. We can rearrange the formula to solve for moles of sucrose since we already have the molarity and volume. Hence moles = molarity x volume = \(0.85 mol/L * 0.05 L\).

Apply the values and calculate

Substitute the volume we calculated in step 1 and the molarity given into the formula in step 2 to find the number of moles of sucrose in the solution. Working through the multiplication gives us 0.0425 moles.

Key concepts

Understanding Molarity

Molarity is an important concept in chemistry. It helps express the concentration of a solute in a solution. Molarity, denoted by the symbol 'M', is calculated by dividing the number of moles of the solute by the volume of the solution in liters.
This gives us the formula:

• \( M = \frac{\text{moles of solute}}{\text{volume of solution (L)}} \)

If you know the molarity and the volume of a solution, you can easily find the amount of solute, in moles, present in the solution. Understanding and calculating molarity is crucial for preparing solutions with precise concentrations required for experiments.
Being accurate with your volume measurements, typically in liters, ensures quality and repeatability when working with solutions in the lab.

Moles: The Chemistry Counting Unit

Moles are a fundamental unit in chemistry used to quantify the amount of a substance. A single mole is Avogadro's number, \(6.022 \times 10^{23}\), of a particular entity, such as atoms, molecules, or ions.
In calculations involving stoichiometry, chemists use moles to relate quantities in chemical reactions and solutions. For example, when dealing with solutions, knowing the number of moles helps determine how concentrated a solution is.
For the problem above, you are tasked with identifying how many moles of sucrose are present in the given solution. Once you have the molarity and the solution's volume, you can easily calculate the number of moles using the formula:

• \( ext{moles} = ext{molarity} \times ext{volume in liters} \)

This calculation reveals how chemistry uses moles as a bridge to connect the macroscopic world with the atomic scale.

Exploring Solutions

Solutions are homogenous mixtures composed of solutes dissolved in solvents. In many laboratory and industrial processes, solutions are used because they enable the precise mixing of substances.
The solute is the substance that is dissolved, and the solvent is the medium in which the solute dissolves. Most often, water is used as a solvent due to its excellent dissolving ability.
In the given exercise, sucrose is the solute, and water acts as the solvent, forming a solution with a specific molarity. To solve problems involving solutions, one must understand how to accurately measure and manipulate them.

• Make sure measurements are precise, typically using liters for volume.
• Know the density of common solvents, such as water, to convert mass to volume if needed.

Understanding solutions and their properties is a cornerstone of stoichiometry and everyday chemical applications.