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Chapter 3: Problem 50

A \(6.01\) -g aqueous solution of isopropyl alcohol contains \(4.01 \mathrm{~g}\) of isopropyl alcohol. What is the mass percentage of isopropyl alcohol in the solution?

Short Answer

Expert verified
The mass percentage of isopropyl alcohol in the solution is 66.72%.

Step by step solution

01

Determine Mass of Solution

The solution contains both isopropyl alcohol and water. We are given that the total mass of the solution is \(6.01\, \text{g}\).
02

Identify Mass of Solute

According to the problem, the mass of isopropyl alcohol (the solute) is \(4.01\, \text{g}\).
03

Set up the Mass Percentage Formula

The mass percentage of a solute in a solution is calculated using the formula: \[ \text{Mass Percentage} = \left( \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \right) \times 100 \]
04

Substitute Values into the Formula

Substitute the given values into the formula: \[ \text{Mass Percentage} = \left( \frac{4.01}{6.01} \right) \times 100 \]
05

Compute the Mass Percentage

Calculate the result of the fraction and then multiply by \(100\) to find the mass percentage: \[ \text{Mass Percentage} = 0.6672 \times 100 = 66.72\% \]

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Key Concepts

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

Isopropyl Alcohol
Isopropyl alcohol is a commonly used type of alcohol in chemical solutions. It is also known as
  • 2-propanol
  • rubbing alcohol
  • propyl alcohol
It is widely known for its disinfectant properties and is used in medical and cleaning supplies.

A unique feature of isopropyl alcohol is its volatility. This means it evaporates quickly; thus, it leaves a cooling effect.

In the exercise you encountered, you looked at a solution where isopropyl alcohol was mixed with water. The focus was on understanding its role as a solute, which is the substance dissolved in a solution.
Solution Composition
The composition of a solution involves both the solute and the solvent. In this exercise, the solution is composed of
  • the solute: isopropyl alcohol
  • the solvent: water
The solution's total mass is the sum of the solute and the solvent masses.

Understanding solution composition is crucial in various applications, including chemistry and pharmaceuticals. Why? Because the concentration affects the solution's effectiveness. For example, if making a disinfectant solution, you'll want the right balance to ensure your mixture works properly.

Mass Percentage

One way to describe solution composition is through mass percentage.

Mass percentage tells you how much of the solution's composition is made up of the solute.
In this case, you used it to measure how much of the mixture is isopropyl alcohol. More mass percentage of isopropyl alcohol means a stronger presence in the solution.
Chemistry Calculations
Chemistry calculations help us quantify the components within a chemical solution. In your exercise, these calculations focused on finding the mass percentage.

Using the Mass Percentage Formula

The mass percentage formula is:
  • Mass Percentage = \( \left( \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \right) \times 100 \)
Let's break down how to use it:

1. **Identify the Solute's Mass**: Start by finding the mass of the solute, which in your exercise is isopropyl alcohol.
This was given as 4.01 grams.2. **Total Solution Mass**: The total mass of the solution in the exercise was 6.01 grams. This includes both the isopropyl alcohol and the water.3. **Substitute and Calculate**: Plug the values into the formula: \( \text{Mass Percentage} = \left( \frac{4.01}{6.01} \right) \times 100 \) 4. **Compute the Result**: This calculation showed the mass percentage of isopropyl alcohol to be 66.72%.

Practical Application

Understanding these calculations empowers you to mix and analyze solutions accurately. This is invaluable in fields such as
  • medicine
  • biochemistry
  • engineering
as it helps ensure the correct concentration strength of various solutions.

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Most popular questions from this chapter

Part 1 a. How many hydrogen and oxygen atoms are present in 1 molecule of \(\mathrm{H}_{2} \mathrm{O} ?\) b. How many moles of hydrogen and oxygen atoms are present in \(1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) ? c. What are the masses of hydrogen and oxygen in \(1.0 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) ? d. What is the mass of \(1.0 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) ? Part 2: Two hypothetical ionic compounds are discovered with the chemical formulas \(\mathrm{XCl}_{2}\) and \(\mathrm{YCl}_{2}\), where \(\mathrm{X}\) and \(\mathrm{Y}\) represent symbols of the imaginary elements. Chemical analysis of the two compounds reveals that \(0.25 \mathrm{~mol} \mathrm{XCl}_{2}\) has a mass of \(100.0 \mathrm{~g}\) and \(0.50 \mathrm{~mol} \mathrm{YCl}_{2}\) has a mass of \(125.0 \mathrm{~g}\). a. What are the molar masses of \(\mathrm{XCl}_{2}\) and \(\mathrm{YCl}_{2}\) ? b. If you had \(1.0\) -mol samples of \(\mathrm{XCl}_{2}\) and \(\mathrm{YCl}_{2}\), how would the number of chloride ions compare? C. If you had \(1.0\) -mol samples of \(\mathrm{XCl}_{2}\) and \(\mathrm{YCl}_{2}\), how would the masses of elements \(\mathrm{X}\) and \(\mathrm{Y}\) compare? d. What is the mass of chloride ions present in \(1.0 \mathrm{~mol} \mathrm{XCl}_{2}\) and \(1.0 \mathrm{~mol} \mathrm{YCl}_{2} ?\) e. What are the molar masses of elements \(\mathrm{X}\) and \(\mathrm{Y}\) ? f. How many moles of \(\mathrm{X}\) ions and chloride ions would be present in a \(200.0-\mathrm{g}\) sample of \(\mathrm{XCl}_{2}\) ? g. How many grams of \(Y\) ions would be present in a \(250.0-\mathrm{g}\) sample of \(\mathrm{YCl}_{2} ?\) h. What would be the molar mass of the compound \(\mathrm{YBr}_{3}\) ? Part 3: A minute sample of \(\mathrm{AlCl}_{3}\) is analyzed for chlorine. The analysis reveals that there are 12 chloride ions present in the sample. How many aluminum ions must be present in the sample? a. What is the total mass of \(\mathrm{AlCl}_{3}\) in this sample? b. How many moles of \(\mathrm{AlCl}_{3}\) are in this sample?

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), burns with the oxygen in air to give carbon dioxide and water. $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ What is the amount (in moles) of water produced from \(0.69 \mathrm{~mol}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} ?\)

Calcium carbide, \(\mathrm{CaC}_{2}\), used to produce acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), is prepared by heating calcium oxide, \(\mathrm{CaO}\), and carbon, \(\mathrm{C}\), to high temperature. $$ \mathrm{CaO}(s)+3 \mathrm{C}(s) \longrightarrow \mathrm{CaC}_{2}(s)+\mathrm{CO}(g) $$ If a mixture contains \(2.60 \mathrm{~kg}\) of each reactant, how many grams of calcium carbide can be prepared?

When dinitrogen pentoxide, \(\mathrm{N}_{2} \mathrm{O}_{5}\), a white solid, is heated, it decomposes to nitrogen dioxide and oxygen. $$ 2 \mathrm{~N}_{2} \mathrm{O}_{5}(s) \stackrel{\Delta}{\longrightarrow} 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) $$ If a sample of \(\mathrm{N}_{2} \mathrm{O}_{5}\) produces \(1.315 \mathrm{~g} \mathrm{O}_{2}\), how many grams of \(\mathrm{NO}_{2}\) are formed?

Zinc metal can be obtained from zinc oxide, \(\mathrm{ZnO}\), by reaction at high temperature with carbon monoxide, \(\mathrm{CO}\). $$ \mathrm{ZnO}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Zn}(s)+\mathrm{CO}_{2}(g) $$ The carbon monoxide is obtained from carbon. $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) $$ What is the maximum amount of zinc that can be obtained from \(75.0 \mathrm{~g}\) of zinc oxide and \(50.0 \mathrm{~g}\) of carbon?
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