Question

An aqueous solution of glucose is \(10 \%\) \((\mathrm{w} / \mathrm{v})\). The volume in which \(1 \mathrm{~mole}\) of glucose is dissolved, will be (a) 181 (b) 91 (c) \(0.91\) (d) \(1.81\)

Short answer

The volume in which 1 mole of glucose is dissolved is 180.16 mL, which is closest to choice (a) 181 mL.

Step-by-step solution

Understand the Percentage Concentration

A solution that is 10% (w/v) means that 10 grams of glucose are present in every 100 mL of solution. This is because (w/v) stands for 'weight per volume'.

Calculate the Molar Mass of Glucose

The molar mass of glucose (C6H12O6) needs to be calculated. Adding up the atomic masses of carbon (C), hydrogen (H), and oxygen (O), the molar mass of glucose is found to be 180.16 g/mol. This means that one mole of glucose weighs 180.16 grams.

Determine Volume for One Mole of Glucose

Since 10 grams are in 100 mL, the volume containing 180.16 grams (1 mole) of glucose can be found by setting up a proportion: (10 g / 100 mL) = (180.16 g / X mL). Solving for X gives the volume in which one mole of glucose is dissolved.

Solve the Proportion

To find the volume X, cross-multiply and solve for X: (10 g) * (X mL) = (180.16 g) * (100 mL), X = (180.16 g * 100 mL) / 10 g. Calculate X to find the volume.

Key concepts

Percentage Concentration

When studying chemistry and working on laboratory experiments, understanding percentage concentration is crucial. This concept expresses the amount of substance present in a given volume or mass of solution. It's commonly represented as weight/volume (w/v), weight/weight (w/w), or volume/volume (v/v). In our particular problem, a 10% (w/v) glucose solution means that for every 100 milliliters of solution we have 10 grams of glucose dissolved.

Percentage concentration can be thought of as a recipe that dictates the strength of a solution. Knowing how to calculate and interpret this concentration is essential for precise scientific work, such as creating solutions with exact properties for experiments or medical purposes. The concept of percentage concentration also lays the foundation for more complex calculations in stoichiometry and solution preparation.

Stoichiometry

At the heart of chemistry lies stoichiometry, the branch that deals with the quantitative relationships between reactants and products in a chemical reaction. Stoichiometry is grounded on the law of conservation of mass where matter is neither created nor destroyed. In practical terms, it allows us to predict how much reactant is needed to form a certain amount of product, and vice versa.

Under the scope of stoichiometry, molar mass is a pivotal concept. It represents the mass of one mole of a substance (the molecular weight expressed in grams) and ties the microscopic world of atoms and molecules to the macroscopic world we can measure. In our exercise, we use the molar mass of glucose to connect the percentage concentration to the volume needed to dissolve one mole of glucose. Here, stoichiometry serves as the bridge from understanding individual components of a reaction to predicting outcomes of chemical processes in a larger scale.

Solution Preparation

The process of solution preparation involves dissolving a solute in a solvent to create a homogeneous mixture or solution. This process is fundamental in chemistry labs, research, and various industries. The steps include determining the desired concentration, calculating the amount of solute needed based on its molar mass, and then measuring and mixing it with the appropriate volume of solvent.

In our case, the preparation of a 10% (w/v) glucose solution requires precision in measurement and an understanding of the calculations behind the proportion of the glucose mass to the volume of the solution. By comprehending the necessary steps and calculations in detail, students can be empowered to prepare accurate solutions, which is an essential skill for many experiments and product formulations. It's crucial to note that attention to detail and strict adherence to calculation results ensure the reproducibility and reliability of scientific experiments involving solutions.