Question

Calculate the amount of solution (g or mL) that contains each of the following amounts of solute: a. \(5.0 \mathrm{~g}\) of \(\mathrm{LiNO}_{3}\) from a \(25 \%(\mathrm{~m} / \mathrm{m}) \mathrm{Li} \mathrm{NO}_{3}\) solution b. \(40.0 \mathrm{~g}\) of \(\mathrm{KOH}\) from a \(10.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{KOH}\) solution c. \(2.0 \mathrm{~mL}\) of formic acid from a \(10.0 \%(\mathrm{v} / \mathrm{v})\) formic acid solution

Short answer

a) 20 g of solution. b) 400 mL of solution. c) 20 mL of solution.

Step-by-step solution

Understanding the problem

The problem requires calculating the total amount of solution needed to obtain a specified amount of solute. The type of concentration percentage (mass/mass, mass/volume, or volume/volume) will determine the steps to solve each part.

Calculating for LiNO3 in a 25% (m/m) solution

For part (a), the solution has a concentration of 25% mass/mass, which means there are 25 grams of \mathrm{LiNO3} in every 100 grams of solution. Setup a proportion to find the total mass of the solution needed for 5.0 grams of \mathrm{LiNO3}. \[ \frac{5.0 \, \mathrm{g} \mathrm{LiNO3}}{x \, \mathrm{g} \, \mathrm{solution}} = \frac{25 \, \mathrm{g} \, \mathrm{LiNO3}}{100 \, \mathrm{g} \, \mathrm{solution}} \] Solve for \( x \): \[ x = \frac{5.0 \, \mathrm{g} \, \mathrm{solution}}{25 / 100} \] \[ x = 20 \, \mathrm{g} \, \mathrm{solution} \]

Calculating for KOH in a 10% (m/v) solution

For part (b), the solution has a concentration of 10% mass/volume, meaning there are 10 grams of \mathrm{KOH} in every 100 milliliters of solution. Setup a proportion to find the total volume of solution needed for 40.0 grams of \mathrm{KOH}. \[ \frac{40.0 \, \mathrm{g} \mathrm{KOH}}{y \, \mathrm{mL} \, \mathrm{solution}} = \frac{10 \, \mathrm{g} \, \mathrm{KOH}}{100 \, \mathrm{mL} \, \mathrm{solution}} \] Solve for \( y \): \[ y = \frac{40.0 \, \mathrm{g} \, \mathrm{KOH}}{10 / 100} \] \[ y = 400 \, \mathrm{mL} \, \mathrm{solution} \]

Calculating for formic acid in a 10% (v/v) solution

For part (c), the solution has a concentration of 10% volume/volume, meaning there are 10 milliliters of formic acid in every 100 milliliters of solution. Setup a proportion to find the total volume of solution needed for 2.0 milliliters of formic acid. \[ \frac{2.0 \, \mathrm{mL} \, \mathrm{formic \, acid}}{z \, \mathrm{mL} \, \mathrm{solution}} = \frac{10 \, \mathrm{mL} \, \mathrm{formic \, acid}}{100 \, \mathrm{mL} \, \mathrm{solution}} \] Solve for \( z \): \[ z = \frac{2.0 \, \mathrm{mL} \, formic \, acid}{10 / 100} \] \[ z = 20 \, \mathrm{mL} \, \mathrm{solution} \]

Key concepts

mass/mass concentration

Mass/mass concentration, often abbreviated as %m/m, is the ratio of the mass of a solute to the mass of the solution, expressed as a percentage. In our example, for a 25% (m/m) LiNO3 solution, this means there are 25 grams of LiNO3 in every 100 grams of the solution. To find the amount of solution needed for a specific mass of solute (e.g., 5.0 grams of LiNO3), you set up a proportion:
\( \frac{5.0 \text{ g LiNO3}}{x \text{ g solution}} = \frac{25 \text{ g LiNO3}}{100 \text{ g solution}} \).
Solving for \( x \) tells you how many grams of the solution you need. Simply put, it's a straightforward way to relate the mass of the solute and the total mass of the solution.

mass/volume concentration

Mass/volume concentration, denoted as %m/v, straddles the units of mass (grams) and volume (milliliters). For example, a 10% (m/v) KOH solution contains 10 grams of KOH per 100 milliliters of solution. To figure out how much solution you need to contain 40.0 grams of KOH, you use:
\( \frac{40.0 \text{ g KOH}}{y \text{ mL solution}} = \frac{10 \text{ g KOH}}{100 \text{ mL solution}} \).
Solving for \( y \) will yield the volume of the solution required. This method is handy, especially in chemistry labs where solutions are frequently measured in volumetric terms despite dealing with solute masses.

volume/volume concentration

Volume/volume concentration, symbolized as %v/v, relates the volume of a solute to the total volume of the solution, measured in milliliters. For a 10% (v/v) formic acid solution, there are 10 milliliters of formic acid per 100 milliliters of solution. To find out how much solution is needed for a certain volume of solute, say 2.0 milliliters of formic acid, set up this proportion:
\( \frac{2.0 \text{ mL formic acid}}{z \text{ mL solution}} = \frac{10 \text{ mL formic acid}}{100 \text{ mL solution}} \).
Solving for \( z \) will give the total volume of the solution. This concept is particularly useful in preparing drinks, perfumes, or other liquid mixtures where both components are liquids.

proportional calculations

Proportional calculations are a cornerstone in solving concentration problems. By setting up ratios and proportions, you can solve for an unknown quantity when you know the relationship between two quantities. Every concentration type (mass/mass, mass/volume, volume/volume) uses this approach. For instance, if you know that 25 grams of LiNO3 in every 100 grams of solution means a 25% concentration, you can find how much of a solution is needed for any given mass of LiNO3 by:
\( \frac{a \text{ g LiNO3}}{x \text{ g solution}} = \frac{25 \text{ g LiNO3}}{100 \text{ g solution}} \).
This method ensures you consistently account for the proportion of solute to solution.

solute and solution relationship

Understanding the relationship between solute and solution is crucial. The solute is the substance dissolved in a solvent to form a solution. The concentration tells you how much solute is present in a certain amount of solution. For example, in a 10% (m/v) KOH solution, 10 grams of KOH are dissolved in enough water to make up 100 milliliters of solution. Knowing this relationship helps in dosing chemicals correctly for desired chemical reactions, medicinal formulations, and even culinary applications. It’s essential to grasp how manipulating either the solute or the solvent affects the concentration and, consequently, the solution’s properties and effectiveness.