Question

Calculate the percent by mass of solute in each of the following solutions. a. \(6.11 \mathrm{mg}\) of calcium chloride dissolved in \(5.25 \mathrm{~g}\) of water b. \(6.11 \mathrm{mg}\) of calcium chloride dissolved in \(52.5 \mathrm{~g}\) of water c. \(6.11 \mathrm{~g}\) of calcium chloride dissolved in \(52.5 \mathrm{~g}\) of water d. \(6.11 \mathrm{~kg}\) of calcium chloride dissolved in \(52.5 \mathrm{~kg}\) of water

Short answer

The percent by mass of solute for each of the solutions is as follows: a. \(0.1162\%\) b. \(0.0116\%\) c. \(10.42\%\) d. \(10.42\%\)

Step-by-step solution

Calculate the total mass of the solution

To find the total mass of the solution, add the mass of solute (calcium chloride) and the mass of solvent (water).

Calculate the mass ratio of solute to solution

Divide the mass of solute by the total mass of the solution to get the mass ratio of solute to the solution.

Find the percent by mass of the solute in the solution

Multiply the mass ratio by 100 to get the percentage of solute in the solution. Let's now apply these steps to the given exercises: a. 6.11 mg of calcium chloride dissolved in 5.25 g of water Step 1: The total mass of the solution is \(6.11 \mathrm{mg} + 5.25 \mathrm{g} = 6.11 \mathrm{mg} + 5250 \mathrm{mg} = 5256.11 \mathrm{mg}\). Step 2: The mass ratio of solute to solution is \(\frac{6.11}{5256.11} = 0.001162\). Step 3: The percent by mass of solute in the solution is \(0.001162 \times 100 = 0.1162\% \). b. 6.11 mg of calcium chloride dissolved in 52.5 g of water Step 1: The total mass of the solution is \(6.11 \mathrm{mg} + 52.5 \mathrm{g} = 6.11 \mathrm{mg} + 52500 \mathrm{mg} = 52506.11 \mathrm{mg}\). Step 2: The mass ratio of solute to solution is \(\frac{6.11}{52506.11} = 0.000116\). Step 3: The percent by mass of solute in the solution is \(0.000116 \times 100 = 0.0116\% \). c. 6.11 g of calcium chloride dissolved in 52.5 g of water Step 1: The total mass of the solution is \(6.11 \mathrm{g} + 52.5 \mathrm{g} = 58.61 \mathrm{g}\). Step 2: The mass ratio of solute to solution is \(\frac{6.11}{58.61} = 0.1042\). Step 3: The percent by mass of solute in the solution is \(0.1042 \times 100 = 10.42\% \). d. 6.11 kg of calcium chloride dissolved in 52.5 kg of water Step 1: The total mass of the solution is \(6.11 \mathrm{kg} + 52.5 \mathrm{kg} = 58.61 \mathrm{kg}\). Step 2: The mass ratio of solute to solution is \(\frac{6.11}{58.61} = 0.1042\). Step 3: The percent by mass of solute in the solution is \(0.1042 \times 100 = 10.42\% \). The percent by mass of solute for each of the solutions is as follows: a. 0.1162% b. 0.0116% c. 10.42% d. 10.42%

Key concepts

Solution Concentration

Understanding solution concentration is crucial in fields ranging from chemistry to culinary arts. Essentially, it tells us how much solute is contained within a solution relative to the quantity of solvent or the total solution. A common measure of this is 'percent by mass' which, for example, indicates the mass of a given solute as a percentage of the total mass of the solution.

To visualize this concept, imagine making lemonade. The sugar you dissolve in water becomes the solute, and the water acts as the solvent. If you're interested in the strength or sweetness of your lemonade, you're considering the concentration. The more sugar you dissolve, the greater the percent by mass, and thus, the higher the concentration of the lemonade. To tailor this to your taste, you're essentially playing with the solution's concentration until it's just right.

Mass Ratio

When it comes to understanding mixtures, the mass ratio is a vital concept. It's the foundation upon which one can calculate percent by mass. In its simplest definition, the mass ratio is the mass of one part of a mixture compared to the mass of the entire mixture.

To bring this to life, let's use a baking example. If a cake recipe requires 200 grams of sugar and 500 grams of flour, the mass ratio of sugar to the total mass (sugar plus flour) would be 200/(200+500). This numerical value is crucial as it gives a direct comparison unaffected by the unit of measurement used. In any measurement system, the ratio remains constant, illustrating a universal relationship between components of a mixture.

Solubility

Solubility might sound like a complicated term, but it describes a simple phenomenon you see all the time. It is the maximum amount of a solute that can dissolve in a given amount of solvent at a specified temperature and pressure, resulting in a saturated solution without any excess solute.

Examples of Solubility

Sugar in tea is a classic example. There’s a limit to how much sugar you can dissolve in your cup of tea; add too much, and you'll see granules sinking to the bottom, indicating that the solution has reached its solubility limit. Solubility varies for different substances and under different conditions, such as temperature. For instance, you can dissolve more sugar in hot water than in cold. This difference is why hot tea can be made sweeter than iced tea with the same amount of water. Understanding solubility can be beneficial for various applications, such as in pharmaceuticals, where the solubility of drugs can determine their effectiveness in the body.