Maki Uses 20 Gallons Of A Solution With An Unknown Ethanol Concentration And 60 Gallons Of A $12\%$ Ethanol Solution To Make 80 Gallons Of A $10\%$ Solution. The Table Shows The Amount Of Each Solution.Ethanol
Introduction
In this article, we will delve into a chemistry problem involving the creation of a solution with a specific ethanol concentration. Maki uses a combination of two solutions with different ethanol concentrations to produce a final solution with a desired concentration. The problem is presented in a table, which we will analyze to determine the unknown ethanol concentration of the initial solution.
The Problem
| Solution | Amount (gallons) | Ethanol Concentration (%) |
|---|---|---|
| Unknown | 20 | x |
| 12% Ethanol | 60 | 12 |
| Final Solution | 80 | 10 |
Maki's goal is to create 80 gallons of a 10% ethanol solution using a combination of the unknown solution and the 12% ethanol solution. We need to find the unknown ethanol concentration of the initial solution.
Setting Up the Equation
Let's denote the unknown ethanol concentration as x. The amount of ethanol in the unknown solution is 20x gallons, and the amount of ethanol in the 12% ethanol solution is 60 * 0.12 = 7.2 gallons. The total amount of ethanol in the final solution is 80 * 0.10 = 8 gallons.
We can set up an equation based on the fact that the total amount of ethanol in the final solution is the sum of the ethanol in the unknown solution and the 12% ethanol solution:
20x + 7.2 = 8
Solving the Equation
To solve for x, we need to isolate the variable. First, let's subtract 7.2 from both sides of the equation:
20x = 8 - 7.2 20x = 0.8
Next, let's divide both sides of the equation by 20:
x = 0.8 / 20 x = 0.04
Conclusion
The unknown ethanol concentration of the initial solution is 4%. This means that the initial solution contains 4% ethanol.
Discussion
This problem involves the concept of concentration and the ability to mix solutions with different concentrations to achieve a desired concentration. It requires the use of algebraic equations to solve for the unknown concentration.
Real-World Applications
This problem has real-world applications in various fields, such as chemistry, biology, and engineering. For example, in the production of pharmaceuticals, it is essential to control the concentration of active ingredients in solutions. Similarly, in the food industry, the concentration of ingredients in solutions can affect the final product's quality and safety.
Tips and Tricks
When solving problems like this, it's essential to:
- Read the problem carefully and understand what is being asked.
- Set up an equation based on the given information.
- Use algebraic techniques to solve for the unknown variable.
- Check the solution by plugging it back into the original equation.
By following these tips and tricks, you can become proficient in solving problems like this and apply the concepts to real-world scenarios.
Final Thoughts
In conclusion, Maki's ethanol solution problem is a classic example of a chemistry problem that requires the use of algebraic equations to solve. By following the steps outlined in this article, you can solve similar problems and apply the concepts to real-world scenarios. Remember to always read the problem carefully, set up an equation, and use algebraic techniques to solve for the unknown variable.
Introduction
In our previous article, we delved into a chemistry problem involving the creation of a solution with a specific ethanol concentration. Maki uses a combination of two solutions with different ethanol concentrations to produce a final solution with a desired concentration. In this article, we will provide a Q&A section to further clarify the concepts and provide additional insights.
Q&A
Q: What is the unknown ethanol concentration of the initial solution?
A: The unknown ethanol concentration of the initial solution is 4%.
Q: How did you arrive at the solution?
A: We set up an equation based on the fact that the total amount of ethanol in the final solution is the sum of the ethanol in the unknown solution and the 12% ethanol solution. We then solved for the unknown variable using algebraic techniques.
Q: What is the significance of the 12% ethanol solution?
A: The 12% ethanol solution serves as a reference point for the concentration of ethanol in the final solution. By using this solution, we can determine the amount of ethanol needed to achieve the desired concentration.
Q: How does this problem relate to real-world applications?
A: This problem has real-world applications in various fields, such as chemistry, biology, and engineering. For example, in the production of pharmaceuticals, it is essential to control the concentration of active ingredients in solutions. Similarly, in the food industry, the concentration of ingredients in solutions can affect the final product's quality and safety.
Q: What are some common mistakes to avoid when solving problems like this?
A: Some common mistakes to avoid include:
- Not reading the problem carefully and understanding what is being asked.
- Not setting up an equation based on the given information.
- Not using algebraic techniques to solve for the unknown variable.
- Not checking the solution by plugging it back into the original equation.
Q: How can I apply the concepts learned from this problem to other areas of chemistry?
A: The concepts learned from this problem can be applied to other areas of chemistry, such as:
- Understanding concentration and the ability to mix solutions with different concentrations to achieve a desired concentration.
- Using algebraic techniques to solve for unknown variables.
- Applying the concepts to real-world scenarios, such as the production of pharmaceuticals or the food industry.
Q: What are some additional tips and tricks for solving problems like this?
A: Some additional tips and tricks include:
- Using a systematic approach to solve the problem.
- Checking the solution by plugging it back into the original equation.
- Using visual aids, such as diagrams or charts, to help understand the problem.
- Breaking down complex problems into smaller, more manageable parts.
Conclusion
In conclusion, Maki's ethanol solution problem is a classic example of a chemistry problem that requires the use of algebraic equations to solve. By following the steps outlined in this article and applying the concepts to real-world scenarios, you can become proficient in solving problems like this and apply the concepts to other areas of chemistry.
Final Thoughts
We hope this Q&A section has provided additional insights and clarification on the concepts learned from Maki's ethanol solution problem. Remember to always read the problem carefully, set up an equation, and use algebraic techniques to solve for the unknown variable. By following these tips and tricks, you can become proficient in solving problems like this and apply the concepts to real-world scenarios.