Question

Calculate the grams or milliliters of solute needed to prepare the following solutions: a. \(150 \mathrm{~mL}\) of a \(40.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{LiNO}_{3}\) solution b. \(450 \mathrm{~mL}\) of a \(2.0 \%(\mathrm{~m} / \mathrm{v})\) KOH solution c. \(225 \mathrm{~mL}\) of a \(15 \%(\mathrm{v} / \mathrm{v})\) isopropyl alcohol solution

Short answer

a) 60 g LiNO₃b) 9 g KOHc) 33.75 mL isopropyl alcohol

Step-by-step solution

Understand the Formula for Solution Concentration

The concentration \((\text{m/v})\) is given by \( \text{concentration} = \frac{\text{mass of solute}}{\text{volume of solution}} \times 100 \), and for \((\text{v/v})\), it is \( \text{concentration} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100 \). We will use these formulas to find the mass or volume of the solute.

Convert Percentage to Decimal for Calculation

For part (a) the % is 40, convert to 0.40. For part (b) the % is 2, convert to 0.02. For part (c) the % is 15, convert to 0.15.

Calculate the Mass of LiNO₃ Needed (Part a)

Using the formula for concentration:\( 40.0 = \frac{\text{mass of solute}}{150 \text{ mL}} \times 100 \)Solving for mass of solute:\( \text{mass of solute} = \frac{40.0 \times 150}{100} = 60 \text{ g LiNO}_{3} \)

Calculate the Mass of KOH Needed (Part b)

Using the formula for concentration:\( 2.0 = \frac{\text{mass of solute}}{450 \text{ mL}} \times 100 \)Solving for mass of solute:\( \text{mass of solute} = \frac{2.0 \times 450}{100} = 9 \text{ g KOH} \)

Calculate the Volume of Isopropyl Alcohol Needed (Part c)

Using the formula for concentration (\text{v/v}):\( 15 = \frac{\text{volume of solute}}{225 \text{ mL}} \times 100 \)Solving for volume of solute:\( \text{volume of solute} = \frac{15 \times 225}{100} = 33.75 \text{ mL isopropyl alcohol} \)

Key concepts

mass/volume concentration

Understanding mass/volume concentration is crucial for preparing solutions in chemistry and biology. This type of concentration tells you how much mass of a solute is dissolved in a given volume of solution. The formula is simple:

\[ \text{Concentration} = \frac{ \text{Mass of Solute} } { \text{Volume of Solution} } \times 100 \]This formula is useful for converting between the percentage concentration and the actual mass of the solute you need to add.

For example, if you have a solution that is 40% mass/volume and you need 150 mL of this solution, you can calculate the mass of the solute like this:
\[ \text{Mass of Solute} = \frac{ 40 \times 150 } { 100 } = 60 \text{ g} \]This tells you that you need to add 60 grams of the solute to 150 mL of solution to get a 40% mass/volume concentration.

Remember:

• Always convert the percentage to a decimal before using it in formulas.
• Mass is usually measured in grams (g).
• Volume is usually measured in milliliters (mL).

volume/volume concentration

Volume/volume concentration is another common way to describe the concentration of a solution. This type of concentration indicates how much volume of a solute is in a given volume of solution. The general formula for volume/volume concentration is:
\[ \text{Concentration} = \frac{ \text{Volume of Solute} } { \text{Volume of Solution} } \times 100 \]This is particularly useful for solutions where both the solvent and solute are liquids.

For instance, if you need to prepare 225 mL of a 15% volume/volume isopropyl alcohol solution, you will calculate the volume of isopropyl alcohol needed as follows:
\[ \text{Volume of Solute} = \frac{ 15 \times 225 } { 100 } = 33.75 \text{ mL} \]This means you need to add 33.75 mL of isopropyl alcohol to get a 15% volume/volume concentration in a 225 mL solution.

Important tips:

• Always turn the percentage into a decimal before calculation.
• Ensure both volumes are measured in the same units (usually mL).

percentage concentration

Percentage concentration is a straightforward way to express the strength of a solution. It tells you the amount of solute present in a specific amount of solution, expressed as a percentage. Depending on the context, it can be either mass/volume or volume/volume concentration.

To make calculations easier, always convert the percentage into a decimal. For example, for a 2% mass/volume potassium hydroxide (KOH) solution, convert the 2% to 0.02.
Then, using the formula:
\[ \text{Concentration} = \frac{ \text{Mass of Solute} } { \text{Volume of Solution} } \times 100 \]If you have 450 mL of this solution, you can calculate the mass of KOH needed like this:
\[ \text{Mass of Solute} = \frac{ 2 \times 450 } { 100 } = 9 \text{ g} \]This means you need 9 grams of KOH to make 450 mL of a 2% solution.

Quick tips:

• Percentage is always out of 100, so multiply or divide accordingly.
• Whether it’s mass/volume or volume/volume, percentage concentration helps in easily visualizing the concentration.