Question

Calculate the mass/mass percent concentration for each of the following solutions. (a) \(20.0 \mathrm{~g} \mathrm{KI}\) in \(100.0 \mathrm{~g}\) of water (b) \(2.50 \mathrm{~g} \mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) in \(95.0 \mathrm{~g}\) of water (c) \(5.57 \mathrm{~g} \mathrm{SrCl}_{2}\) in \(225.0 \mathrm{~g}\) of water (d) \(50.0 \mathrm{~g} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) in \(200.0 \mathrm{~g}\) of water

Short answer

(a) 16.67%, (b) 2.56%, (c) 2.42%, (d) 20.0%

Step-by-step solution

Define Mass/Percent Concentration Formula

The mass/mass percent concentration is calculated using the formula:\[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solute} + \text{mass of solvent}} \right) \times 100 \]

Calculate for KI Solution

For the KI solution, the total mass of the solution is the sum of the mass of KI and the mass of water: \[ \text{Total mass of solution} = 20.0 \, \text{g} + 100.0 \, \text{g} = 120.0 \, \text{g} \]Now, substitute in the formula:\[ \text{Mass percent} = \left( \frac{20.0}{120.0} \right) \times 100 = 16.67\% \]

Calculate for AgC2H3O2 Solution

For the AgC2H3O2 solution, calculate the total mass of the solution: \[ \text{Total mass of solution} = 2.50 \, \text{g} + 95.0 \, \text{g} = 97.5 \, \text{g} \]Now, substitute in the formula:\[ \text{Mass percent} = \left( \frac{2.50}{97.5} \right) \times 100 = 2.56\% \]

Calculate for SrCl2 Solution

For the SrCl2 solution, calculate the total mass of the solution:\[ \text{Total mass of solution} = 5.57 \, \text{g} + 225.0 \, \text{g} = 230.57 \, \text{g} \]Now, substitute in the formula: \[ \text{Mass percent} = \left( \frac{5.57}{230.57} \right) \times 100 = 2.42\% \]

Calculate for C12H22O11 Solution

For the C12H22O11 solution, calculate the total mass of the solution:\[ \text{Total mass of solution} = 50.0 \, \text{g} + 200.0 \, \text{g} = 250.0 \, \text{g} \]Now, substitute into the formula:\[ \text{Mass percent} = \left( \frac{50.0}{250.0} \right) \times 100 = 20.0\% \]

Key concepts

Chemical Solutions

A chemical solution is a homogeneous mixture consisting of two or more substances. The substances within this solution are not chemically bonded, which means that each component retains its original properties. Solutions are all around us—think of saltwater, sugar in coffee, or even air.
What makes solutions unique is how uniform they are across their composition. No matter where you sample it, you'll find the same proportion of its components.

• Simplest Form: Typically, solutions are made up of a solute dissolved into a solvent.
• Examples in Daily Life: Drinks, air, and cleaning detergents.

Understanding solutions sets the stage for learning about their components and properties in more detail.

Solute and Solvent

In any given solution, you have a solute and a solvent. The solvent is the substance that does the dissolving, frequently present in a larger quantity. Think of this as the medium that hosts the solute. Conversely, the solute is the substance that gets dissolved in the solvent.
It’s similar to making orange juice by dissolving the powder (solute) into water (solvent).

• Solvent Role: host medium for the solute, determining the state (liquid, solid, or gas) of the solution.
• Example of Solvents: Water is often called the "universal solvent" due to its high ability to dissolve many substances.
• Example of Solutes: Salt, sugar, and gases like oxygen in water.

The nature of both solute and solvent impacts the properties of the final mixture.

Mass/Mass Percent Calculation

The mass/mass percent concentration is a measure of how much solute is present in a given amount of solution, expressed as a percentage. It's calculated by comparing the mass of the solute to the total mass of the solution.
This calculation is crucial in fields like chemistry and pharmacy, to ensure the correct concentration of components.

Here's the step-by-step process:

• Identify the mass of the solute.
• Add the solute's mass to the solvent's mass to find the total mass of the solution.
• Use this formula: \[\text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solute} + \text{mass of solvent}} \right) \times 100\]

By determining the mass percent, you can adjust solution concentrations precisely for experiments or manufacturing needs.