Question

A solution that is \(9 \%\) by mass glucose contains \(9 \mathrm{g}\) of glucose in every ________ g of solution.

Short answer

A solution that is \(9\%\) by mass glucose contains \(9 \mathrm{g}\) of glucose in every \(100 \mathrm{g}\) of solution.

Step-by-step solution

Determine the percentage of glucose by mass in the solution

Given that the solution is 9% by mass glucose, it means 9g of glucose is present in every 100g of solution. To find the total mass of the solution, we can use the formula: Percentage of glucose = (Mass of glucose / Total mass of the solution) × 100

Plug the values into the formula

Now let's plug the given values into the formula: 9 = (9 / Total mass of the solution) × 100

Solve for the total mass of the solution

To find the total mass of the solution, we need to solve for it in the equation: 9 × (Total mass of the solution) = 9 × 100 Divide both sides by 9 to isolate the "Total mass of the solution" variable: Total mass of the solution = (9 × 100) / 9

Calculate the total mass of the solution

Now we can calculate the total mass of the solution: Total mass of the solution = (9 × 100) / 9 Total mass of the solution = 900 / 9 Total mass of the solution = 100 So, the solution that is 9% by mass glucose contains 9g of glucose in every 100g of the solution.

Key concepts

Concentration of Solutions

Understanding the concentration of solutions is essential for fields ranging from chemistry to cooking. Concentration refers to how much of a substance, known as the solute, is contained in a specific amount of solvent. This can be expressed in various ways, such as molarity, molality, or mass percentage.

In day-to-day terms, the concept of concentration can be thought of like how strong your tea is; the more tea leaves you use for a given amount of water, the stronger, or more concentrated, the tea becomes. In the context of our example with glucose, when a solution is described as '9 percent by mass,' it is referring to the concentration of glucose within that mixture. This is a mass percentage, a common way to express concentration in chemistry.

Mass Percentage

Mass percentage, also known as percent by weight, is a way of representing concentration by showing the mass of the solute in proportion to the total mass of the solution. To calculate the mass percentage, you divide the mass of the solute by the total mass of the solution and then multiply the result by 100 to get a percentage.

In the exercise example, the mass percentage of glucose in the solution is 9%. This means that for every 100 grams of the solution, 9 grams are glucose. If a student were to struggle with this concept, it might be helpful to visualize it through a real-world analogy, such as a mixture of 9 grams of salt in 100 grams of water—a 9% salt solution.

Stoichiometry

Stoichiometry is the method used in chemistry to calculate the relative quantities of reactants and products involved in chemical reactions. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed during a chemical reaction. Thus, the mass of the reactants must equal the mass of the products.

To solve stoichiometry problems, one must be familiar with the mole concept and be able to write and interpret balanced chemical equations. The process often involves converting between grams, moles, and molecules using the molecular weight as a conversion factor. If students get stuck on stoichiometry problems, encouraging them to approach the problem step by step and keeping track of units often helps with clarity and prevents confusion.