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Chapter 4: Problem 27

Describe the preparation of (a) \(500 \mathrm{~mL}\) of \(4.75 \%(\mathrm{w} / \mathrm{v})\) aqueous ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, 46.1 \mathrm{~g} / \mathrm{mol}\right)\). (b) \(500 \mathrm{~g}\) of \(4.75 \%(w / w)\) aqueous ethanol. (c) \(500 \mathrm{~mL}\) of \(4.75 \%(\mathrm{v} / \mathrm{v})\) aqueous ethanol.

Short Answer

Expert verified
(a) Use 23.75 g ethanol; (b) use 23.32 g ethanol; (c) use 23.75 mL ethanol.

Step by step solution

01

Understanding %(w/v) Calculation

To calculate %(w/v), use the formula: \[ \%( ext{w/v}) = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100 \% \]For this problem, the desired concentration is \(4.75 \%\), and the total volume is \(500 \text{ mL}\). Rearrange to find the mass of ethanol needed:\[ \text{mass of ethanol} = \frac{4.75}{100} \times 500 = 23.75 \text{ g} \].
02

Preparing 500 mL of %(w/v) Solution

Measure 23.75 g of ethanol and dissolve it in water. Add water to reach a total volume of 500 mL. Ensure the solution is well mixed.
03

Understanding %(w/w) Calculation

To calculate %(w/w), use the formula:\[ \%( ext{w/w}) = \frac{\text{mass of solute (g)}}{\text{mass of solution (g)}} \times 100 \% \]Here, the desired concentration is \(4.75\%\), and the total mass is \(500 \text{ g}\). Rearrange to find the mass of ethanol needed:\[ \text{mass of ethanol} = \frac{4.75}{100 + 4.75} \times 500 \approx 23.32 \text{ g} \].
04

Preparing 500 g of %(w/w) Solution

Measure 23.32 g of ethanol and add it to a container. Add water until the total mass is 500 g. Mix thoroughly to ensure a uniform solution.
05

Understanding %(v/v) Calculation

For %(v/v), the formula is:\[ \%( ext{v/v}) = \frac{\text{volume of solute (mL)}}{\text{volume of solution (mL)}} \times 100 \% \]Here, the desired concentration is \(4.75\%\), and the total volume is 500 mL. Rearrange to find the volume of ethanol needed:\[ \text{volume of ethanol} = \frac{4.75}{100} \times 500 = 23.75 \text{ mL} \].
06

Preparing 500 mL of %(v/v) Solution

Measure 23.75 mL of ethanol and dilute it with water to a final volume of 500 mL. Mix the solution thoroughly to ensure even distribution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percent Concentration
Percent concentration is a way to express how much solute is present in a solution. It is calculated as the percentage of the solute in terms of its mass or volume, compared to the total mass or volume of the solution.
Here are the most common types of percent concentration:
  • Weight/Volume (% w/v): This is the mass of solute divided by the volume of the solution, multiplied by 100%.
  • Weight/Weight (% w/w): This involves the mass of the solute divided by the total mass of the solution, multiplied by 100%.
  • Volume/Volume (% v/v): This is the volume of the solute divided by the total volume of the solution, multiplied by 100%.
Understanding these different types of percent concentration is crucial for preparing solutions accurately in laboratories and other scientific applications.
Aqueous Ethanol
Aqueous ethanol solutions are mixtures where ethanol, or ethyl alcohol ( "C_2H_5OH" ), is the solute, and water is the solvent. This type of solution is common in laboratories and industries.
Ethanol is frequently used because it is a clear alcohol and has the capability of mixing with water in almost any proportion.
Aqueous ethanol solutions are utilized for:
  • Cleaning and sanitizing applications
  • Preparation of tinctures and extracts in pharmaceuticals
  • Solvent in chemical reactions
  • Component in fuels and alcoholic beverages
Understanding how to prepare accurate aqueous ethanol solutions is essential for its effectiveness and safety in various applications.
Mass-Volume Calculation
Mass-volume calculations, expressed as (% w/v), are vital when preparing solutions where solutes are expressed in terms of mass, and solutions are expressed in terms of volume.
For example, if you wish to prepare 500 mL of a 4.75% (w/v) aqueous ethanol solution, you need to determine how much ethanol is required:
  • Use the formula: \[ \%( w/v ) = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \times 100 \% \]
  • Rearrange to find the mass: \[ \text{mass of ethanol} = \frac{4.75}{100} \times 500 = 23.75 \, \text{g} \]
The procedure then includes dissolving the ethanol in water, and ensuring the total solution volume is exactly 500 mL. This ensures a precise concentration.
Mass-Mass Calculation
Mass-mass calculations, or (% w/w), are used when both the solute and the solution are expressed in terms of mass. This method is practical when it is crucial to maintain a certain mass ratio.For instance, to create 500 g of a 4.75% (w/w) aqueous ethanol solution, you need to calculate the mass of ethanol required:
  • Apply this formula: \[ \%( w/w ) = \frac{\text{mass of solute (g)}}{\text{mass of solution (g)}} \times 100 \% \]
  • Rearrange to find the mass: \[ \text{mass of ethanol} = \frac{4.75}{100 + 4.75} \times 500 \approx 23.32 \, \text{g} \]
Then, add the measured quantity of ethanol to a container, and top up with water until the total mass reaches 500 g.
Volume-Volume Calculation
Volume-volume calculations, expressed as (% v/v), become necessary when expressing solute and solution in terms of volume. It is particularly useful for liquid solutes.For example, preparing 500 mL of a 4.75% (v/v) aqueous ethanol solution requires you to calculate the ethanol volume needed:
  • Use the formula: \[ \%( v/v ) = \frac{\text{volume of solute (mL)}}{\text{volume of solution (mL)}} \times 100 \% \]
  • Rearrange to find the volume: \[ \text{volume of ethanol} = \frac{4.75}{100} \times 500 = 23.75 \, \text{mL} \]
Pour this volume of ethanol into a measuring cylinder, dilute with water until the total volume reaches 500 mL, ensuring uniform mixing for accurate concentration.

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Most popular questions from this chapter

What mass of solid \(\mathrm{La}\left(\mathrm{IO}_{3}\right)_{3}(663.6 \mathrm{~g} / \mathrm{mol})\) is formed when \(50.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{La}^{3+}\) are mixed with \(75.0 \mathrm{~mL}\) of \(0.302 \mathrm{M} \mathrm{IO}_{3}{ }^{-}\)?

Exactly \(75.00 \mathrm{~mL}\) of a \(0.3132 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) were treated with \(150.0 \mathrm{~mL}\) of \(0.4025 \mathrm{M} \mathrm{HClO}_{4}\) and boiled to remove the \(\mathrm{SO}_{2}\) formed. (a) What was the mass in grams of \(\mathrm{SO}_{2}\) that was evolved? (b) What was the concentration of the unreacted reagent \(\left(\mathrm{Na}_{2} \mathrm{SO}_{3}\right.\) or \(\left.\mathrm{HClO}_{4}\right)\) after the reaction was complete?

Describe the preparation of \(750 \mathrm{~mL}\) of \(6.00 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) from the commercial reagent that is \(86 \% \mathrm{H}_{3} \mathrm{PO}_{4}\) (w/w) and has a specific gravity of \(1.71\).

What volume of \(0.01000 \mathrm{M} \mathrm{AgNO}_{3}\) would be required to precipitate all of the \(\mathrm{I}^{-}\)in \(200.0 \mathrm{~mL}\) of a solution that contained \(24.32 \mathrm{ppt} \mathrm{KI}\) ?

What is the mass in grams of solute in *(a) \(250 \mathrm{~mL}\) of \(0.264 \mathrm{M} \mathrm{H}_{2} \mathrm{O}_{2}\) ? *(b) \(37.0 \mathrm{~mL}\) of \(5.75 \times 10^{-4} \mathrm{M}\) benzoic acid (122 \(\left.\mathrm{g} / \mathrm{mol}\right)\) ? (c) \(4.50 \mathrm{~L}\) of a solution that contains \(31.7 \mathrm{ppm}\) of \(\mathrm{SnCl}_{2}\) ? (d) \(11.7 \mathrm{~mL}\) of \(0.0225 \mathrm{M} \mathrm{KBrO}_{3}\) ?
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