Problem 40 - Chemistry The Molecular Science

Question

Calculate the mass (g) of sucrose in \(1.0 \mathrm{~kg}\) of a \(0.25 \%\) sucrose solution.

Step-by-Step Solution

Answer

2.5 grams of sucrose.

Step 1: Understand Percent Concentration

The problem involves a 0.25% concentration, which means there are 0.25 grams of sucrose in every 100 grams of solution. We need to calculate how much sucrose is in 1.0 kg (or 1000 grams) of this solution.

Step 2: Convert Mass of Solution to Grams

The total mass of the solution given is 1.0 kg. To convert kilograms to grams, we multiply by 1000:\[1.0 \text{ kg} = 1000 \text{ grams}\]

Step 3: Calculate Mass of Sucrose

Using the percent concentration, calculate the mass of sucrose in the 1000 grams solution. Since the concentration is 0.25%, the mass of sucrose is:\[\frac{0.25}{100} \times 1000 = 2.5 \text{ grams}\]

Key Concepts

Understanding Percent Concentration in Solutions

Percent concentration is a simple way to express how much solute (in this case, sucrose) is present in a solution. When we talk about a 0.25% sucrose solution, it means there are 0.25 grams of sucrose dissolved in every 100 grams of the solution. This is a key concept because it helps us determine how much of the solute exists in larger or smaller amounts of solution.
Percentages are helpful because they provide a quick understanding of the ratio of solute to solution. This method is widely used in chemistry for preparing various solutions with precise concentrations.
To use percent concentration effectively, it's crucial to remember that it is always based on a per 100 unit of the total solution. So, anytime you want to find out the absolute mass of the solute in a different total mass of solution, you'll relate it back to this fundamental principle.

The Importance of Mass Conversion

Mass conversion is an important step in many calculations involving concentrations. Often, the mass of a solution is provided in units like kilograms, but we might need it in grams for our concentration calculations.
In this exercise, the mass is given as 1.0 kg, and we need to convert this into grams to match the units of our percent concentration. The conversion is straightforward: you multiply by 1000, because there are 1000 grams in a kilogram. Thus, 1.0 kg becomes 1000 grams.
Always remember that converting units is crucial when performing calculations to ensure consistency and accuracy. Plus, it allows you to directly apply the percent concentration values given, without additional complications.

Calculating Sucrose in a Solution

When faced with a problem requiring the calculation of the mass of sucrose in a solution, understanding both percent concentration and mass conversion is essential.
In our situation, with a 0.25% sucrose solution, we determine how much sucrose is in 100 grams of solution (0.25 grams) and then apply this ratio to the total mass of the solution we're interested in.
By multiplying the percent concentration (0.25) by the total grams of the solution (1000 grams), and then dividing by 100, we find the solution contains 2.5 grams of sucrose.
This approach allows for precise calculation of solute mass, ensuring accurate formulation and preparation of chemical solutions in both educational and professional settings. Remember, the percent figure represents the grams of solute per 100 grams of solution, making it transferable to any amount simply by scaling up or down.