Ch.9 Solutions

Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 14th Edition

Timberlake14th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9781292472249당신이 사용하는 게 아니라요?교과서 변경

Timberlake 14th Edition

Ch.9 Solutions

문제 61

9장, 문제 61

You need 500. mL of a 5.0% (m/v) glucose solution. If you have a 25% (m/v) glucose solution on hand, how many milliliters do you need?

검증된 단계별 안내

Step 1: Understand the problem. You are tasked with preparing 500. mL of a 5.0% (m/v) glucose solution using a 25% (m/v) glucose solution. This is a dilution problem, where you will use the dilution equation:

C_{1} V_{1} = C_{2} V_{2}

, where

C_{1}

and

V_{1}

are the concentration and volume of the stock solution, and

C_{2}

and

V_{2}

are the concentration and volume of the diluted solution.

Step 2: Assign the known values to the variables in the dilution equation. The stock solution has a concentration of

C_{1} = 25%

(m/v), and you need to find the volume of this stock solution,

V_{1}

. The diluted solution has a concentration of

C_{2} = 5.0%

(m/v) and a volume of

V_{2} = 500.

mL.

Step 3: Rearrange the dilution equation to solve for

V_{1}

, the volume of the stock solution needed. The equation becomes:

V_{1} = (C_{2} V_{2})/ C_{1}

Step 4: Substitute the known values into the rearranged equation. This gives:

V_{1} = (5.0% × 500. mL) / 25%

. Ensure that the units and percentages are consistent throughout the calculation.

Step 5: Perform the calculation to determine the value of

V_{1}

. This will give you the volume of the 25% (m/v) glucose solution required to prepare the desired 5.0% (m/v) glucose solution.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Mass/Volume Percentage (m/v)

Mass/volume percentage (m/v) is a concentration unit that expresses the mass of solute in grams per 100 mL of solution. For example, a 5.0% (m/v) glucose solution contains 5 grams of glucose in 100 mL of solution. Understanding this concept is crucial for calculating how much of a concentrated solution is needed to achieve a desired concentration.

Dilution Principle

The dilution principle states that the concentration of a solution can be altered by adding more solvent or mixing it with another solution. The relationship can be expressed using the formula C1V1 = C2V2, where C1 and V1 are the concentration and volume of the initial solution, and C2 and V2 are the concentration and volume of the final solution. This principle is essential for determining how to prepare solutions of specific concentrations.

Volume Calculation

Volume calculation involves determining the amount of liquid required to achieve a specific concentration. In this context, it requires calculating how many milliliters of a higher concentration solution (25% m/v) are needed to create a lower concentration solution (5% m/v) in a total volume of 500 mL. Mastery of volume calculations is vital for accurate solution preparation in laboratory settings.