Question

How many grams of \(\mathrm{CuCl}_{2}\) are required to prepare 1250. g of a \(1.25 \%\) (by mass) \(\mathrm{CuCl}_{2}\) solution?

Short answer

Approximately 15.625 g of \(\mathrm{CuCl}_{2}\) is required to prepare 1250 g of a 1.25% (by mass) \(\mathrm{CuCl}_{2}\) solution.

Step-by-step solution

Convert the percentage to a decimal

To convert the given percentage (1.25%) to a decimal, we can divide it by 100. \(Decimal\,of\,1.25\% = \frac{1.25}{100}\)

Calculate the mass of \(\mathrm{CuCl}_{2}\) in the solution

Now that we have the decimal, we can find the mass of \(\mathrm{CuCl}_{2}\) by multiplying the decimal with the total mass of the solution. \[Mass\,of\,\mathrm{CuCl}_{2} = decimal \times total\,mass\,of\,solution\] \[Mass\,of\,\mathrm{CuCl}_{2} = \frac{1.25}{100} \times 1250 g\]

Calculate the final answer

Now, we can calculate the mass of \(\mathrm{CuCl}_{2}\) required to prepare the given solution. \[Mass\,of\,\mathrm{CuCl}_{2} = \frac{1.25}{100} \times1250 g ≈ 15.625 g\] Approximately 15.625 g of \(\mathrm{CuCl}_{2}\) is required to prepare 1250 g of a 1.25% (by mass) \(\mathrm{CuCl}_{2}\) solution.

Key concepts

Mass-to-Mass Conversion

Mass-to-mass conversion is a fundamental concept in chemistry. It involves converting a percentage concentration in a solution to an actual mass of solute needed. When we say "mass percent," we're referring to the mass of a solute per 100 grams of solution. Let's consider that you have a solution that's 1.25% CuCl₂ by mass. This means there are 1.25 grams of CuCl₂ for every 100 grams of solution. It's like breaking down a pie into smaller slices—each slice representing a mass of the solute proportional to the whole pie. To find how many grams of a solute you need in a larger solution, simply multiply your target percentage (expressed as a decimal) by the total mass of your solution. Using our example, you'd multiply 0.0125 (which is 1.25% divided by 100) by the target solution mass of 1250 grams. This simple multiplication helps quickly identify how much of the substance you need.

Solution Concentration

Solution concentration expresses the amount of solute present in a given amount of solvent or solution. It can be measured in various ways, including mass percent, molarity, and part per million. Mass percent is a way to express solution concentration that indicates the mass of solute divided by the total mass of the solution, then multiplied by 100 to get a percentage. Concentration can impact the properties of a solution, such as its boiling and freezing points. For instance, a 1.25% CuCl₂ solution would have different properties than a solution with higher or lower concentrations. This is why understanding concentration is crucial in fields like chemistry and medicine, where precise measurements are necessary for reactions or treatments. In our exercise, concentration is determined by the mass of solute (CuCl₂) against the total mass of the solution (1250 g). This got us to 15.625 g of CuCl₂ needed.

Chemical Calculations

Chemical calculations, like finding the amount of solute needed, are essential to chemistry. They help in determining exact amounts for reactions to occur correctly and safely. These calculations often involve conversion processes, such as converting percentages to masses, moles, or volumes, ensuring consistency across chemical reactions. Understanding how to correctly perform these calculations can refine your experimental design and avoid discrepancies. Calculation problems frequently use algebraic formulas and proportional relationships, which are key to finding the mass of a reactant or product required or produced. In this problem, you first converted the percentage to a decimal to find the mass needed. Repeating processes such as this makes balancing equations more manageable and teaches invaluable problem-solving skills. Starting with the given percentage, then multiplying by the solution's mass, is a fundamental skill for anyone stepping into chemistry.