Question

If 20.0 gallons of gasohol contains 2.40 gal of ethanol, what is the percent of alcohol in the gasohol?

Short answer

The percentage of ethanol in the gasohol is 12%.

Step-by-step solution

Understand the Components

Gasohol is a fuel made up of gasoline and ethanol. In this problem, we're provided with 20.0 gallons of gasohol that contains 2.40 gallons of ethanol. Our goal is to find the percentage of ethanol in the gasohol mixture.

Calculate the Percentage

The percentage of ethanol in the gasohol is calculated using the formula: \[\text{Percent of Ethanol} = \left(\frac{\text{Volume of Ethanol}}{\text{Total Volume of Gasohol}}\right) \times 100\]In this case, the volume of ethanol is 2.40 gallons and the total volume of gasohol is 20.0 gallons.

Substitute Values into the Formula

Substitute the known values into the percentage formula: \[\text{Percent of Ethanol} = \left(\frac{2.40}{20.0}\right) \times 100\]

Compute the Calculation

First calculate the division: \[\frac{2.40}{20.0} = 0.12\]Then, multiply by 100 to convert to a percentage: \[0.12 \times 100 = 12\%\]

Conclusion

The final answer is that the ethanol composes 12% of the gasohol.

Key concepts

Ethanol Calculation

Determining the percent of ethanol in a mixture like gasohol is straightforward but crucial, especially when dealing with fuel efficiency and environmental concerns. Let's break down how this calculation is performed.
To find out the percentage of ethanol, the formula used is:

• \( \text{Percent of Ethanol} = \left(\frac{\text{Volume of Ethanol}}{\text{Total Volume of Gasohol}}\right) \times 100 \)

In this formula, you simply replace the placeholders with the actual numbers you have. So if 2.40 gallons of ethanol are mixed with gasoline to make up a total of 20.0 gallons of gasohol, the calculation is:

• First, divide the volume of ethanol by total volume: \( \frac{2.40}{20.0} = 0.12 \)
• Then, multiply by 100 to convert the decimal to a percentage: \( 0.12 \times 100 = 12\% \)

This shows that ethanol constitutes 12% of the gasohol mixture.
By understanding each step, the ethanol calculation becomes a breeze to handle, ensuring accurate results.

Gasohol

Gasohol is a widely used fuel mixture, known for combining gasoline and ethanol. This blend is significant for various reasons, especially given today's focus on renewable energy resources.
Typically, gasohol can have different ratios, but a common mixture is about 10% ethanol and 90% gasoline. The inclusion of ethanol in gasoline:

• Boosts the octane rating, which improves engine performance.
• Reduces greenhouse gas emissions, contributing to a cleaner environment.
• Utilizes renewable resources, making it a more sustainable choice than purely fossil-based fuels.

The proportions in gasohol affect both its energy content and environmental benefits, highlighting why accurately calculating the ethanol percentage is vital.
This understanding not only helps students with their exercises but also gives insights into why fuel compositions matter in today's world.

Mixture Problems

Mixture problems are common in mathematics and science, focusing on combining different substances to create a solution or mixture with specific properties.
These problems often involve determining the concentration or percentage of components within a mixture. The key to solving mixture problems lies in:

• Clearly understanding what components are involved in the mixture.
• Knowing the total volume or mass of the mixture.
• Using the correct formula for the scenario at hand, often involving ratios or percentages.

In the case of ethanol and gasohol, understanding mixture problems allows one to precisely determine how much ethanol is present, which is crucial for both academic exercises and practical applications, such as in blending fuels.
Tackling these problems enhances critical thinking and quantitative reasoning skills by requiring a structured approach to problem-solving.