Question

Consider a solution of glucose in water that is \(5.25 \%\) by mass glucose. Calculate the indicated quantities. a. the mass of glucose in \(225 \mathrm{g}\) of the solution b. the number of grams of glucose needed to prepare \(225 \mathrm{g}\) of the solution c. the amount of solution needed to obtain \(35.0 \mathrm{g}\) of glucose d. the mass of water contained in 225 g of the solution

Short answer

a) There are 11.8125g of glucose in 225g of the solution. b) We need 11.8125g of glucose to prepare 225g of the solution. c) We need 666.67g of the solution to obtain 35.0g of glucose. d) The mass of water contained in 225g of the solution is 213.1875g.

Step-by-step solution

a. Find the mass of glucose in 225g of the solution.

Given the solution concentration as 5.25% by mass which means, in 100g of the solution, there are 5.25g of glucose. Now we need to find how many grams of glucose are present in 225g of the solution. We can do this by setting up a proportion: \(\frac{5.25g\ of\ glucose}{100g\ of\ solution} = \frac{xg\ of\ glucose}{225g\ of\ solution}\) Solve for x: \(x = \frac{5.25g \times 225g}{100g} = 11.8125g\) Thus, there are 11.8125g of glucose in 225g of the solution.

b. Find the number of grams of glucose needed to prepare 225g of the solution.

Since the 225g of the solution we just calculated contains 11.8125g of glucose, we need that same amount of glucose to prepare 225g of the solution. So, we need 11.8125g of glucose to prepare 225g of the solution.

c. Find the amount of solution needed to obtain 35.0g of glucose.

In this part of the problem, we are given the mass of glucose we want to obtain (35.0g) and need to find the mass of the entire solution that contains this amount of glucose. We can use the solution concentration to set up another proportion: \(\frac{5.25g\ of\ glucose}{100g\ of\ solution} = \frac{35.0g\ of\ glucose}{xg\ of\ solution}\) Solve for x: \(x = \frac{35.0g \times 100g}{5.25g} = 666.67g\) Thus, we need 666.67g of the solution to obtain 35.0g of glucose.

d. Find the mass of water contained in 225g of the solution.

To find the mass of water in the solution, we need to subtract the mass of glucose in the solution from the total mass of the solution. Mass of glucose in 225g of the solution = 11.8125g (from part a) Total mass of the solution = 225g Mass of water = Total mass of the solution - Mass of glucose Mass of water = \(225g - 11.8125g = 213.1875g\) Thus, the mass of water contained in 225g of the solution is 213.1875g.

Key concepts

Percent by Mass

When we talk about the 'percent by mass' of a solution, we are describing the concentration of a solute (in this case, glucose) in a solvent (water). It is expressed as the mass of the solute divided by the total mass of the solution, multiplied by 100 to get a percentage.

For example, if a solution contains 5.25% glucose by mass, this means that in every 100 grams of this solution, there is 5.25 grams of glucose. To calculate the mass of glucose in any other mass of the solution, you use a simple proportion based on the percent by mass, as shown in the exercise.

It's crucial for students to understand how to convert between the mass of the solute, the mass of the solution, and the percent by mass, as this is a foundational concept in chemistry that applies to the preparation and analysis of mixtures.

Stoichiometry

Stoichiometry is the study of the quantitative relationships, or ratios, between the reactants and products in chemical reactions. In terms of concentration calculations, it helps you understand the proportion of substances involved.

Understanding stoichiometry is essential when preparing solutions or when reacting substances because it allows you to predict the amounts of products that can be formed from given reactants, or the amounts of reactants needed to create a certain amount of product. In this exercise, stoichiometry would be used if you were to calculate how much water and glucose are needed to create a solution of a certain concentration.

Mass-to-Mass Conversions

Mass-to-mass conversions are a type of stoichiometric calculation. They involve converting mass units of one substance to the equivalent mass units of another, based on their stoichiometric relationship.

In the context of our exercise, you're essentially asked to perform mass-to-mass conversions when you calculate the amount of glucose in a certain mass of solution (from the percent by mass) or when you calculate the amount of solution needed to obtain a certain mass of glucose. The basis of this calculation is the proportionality derived from the percent by mass. These conversions form the core of many chemical calculation problems involving the preparation and analysis of compounds.

Solution Preparation

Solution preparation involves accurately creating a solution with a specific concentration. To prepare a solution, one must measure out a specific amount of solute (like glucose) and dissolve it in a solvent (like water) until the solution reaches a desired volume or mass.

Knowing the percent by mass of a solution enables you to determine how much solute to add to a certain amount of solvent to achieve the required concentration. As in our exercise, if you want to prepare a 225 g solution of 5.25% glucose by mass, you must calculate the required glucose mass and mix it with the appropriate amount of water. Solution preparation is a fundamental skill in chemistry labs, as it ensures that reactions occur correctly and with predictable results. Careful calculations and precise measurement are vital in achieving the desired solution concentration.