A Chemist Mixes 4 Liters Of One Acid Solution With 10 Liters Of A $40\%$ Solution, Resulting In A $30\%$ Acid Solution. The Table Shows The Amount Of Each Solution Used.$\[ \begin{array}{|c|c|c|c|} \hline & \text{Liters} &
A Chemist's Acid Solution Conundrum: A Problem of Mixture and Percentage
In the world of chemistry, mixtures and solutions are a crucial aspect of various experiments and processes. A chemist's ability to accurately calculate the concentration of a solution is essential in ensuring the success of their experiments. In this article, we will delve into a problem involving the mixing of two acid solutions, resulting in a 30% acid solution. We will explore the concept of mixture and percentage, and provide a step-by-step solution to the problem.
A chemist mixes 4 liters of one acid solution with 10 liters of a 40% solution, resulting in a 30% acid solution. The table below shows the amount of each solution used.
| Liters | Acid Content | |
|---|---|---|
| Solution 1 | 4 | 0% (assuming) |
| Solution 2 | 10 | 40% |
| Resulting Solution | 14 | 30% |
To solve this problem, we need to understand the concept of mixture and percentage. When two solutions are mixed, the resulting solution will have a concentration that is a weighted average of the concentrations of the two original solutions. In this case, we are given the concentrations of the two original solutions (40% and 0%) and the resulting solution (30%). We need to find the amount of acid in each solution.
Step 1: Calculate the Amount of Acid in Solution 2
Solution 2 has a concentration of 40% and a volume of 10 liters. To find the amount of acid in Solution 2, we can multiply the concentration by the volume.
acid_in_solution_2 = 0.4 * 10
print(acid_in_solution_2)
Step 2: Calculate the Amount of Acid in the Resulting Solution
The resulting solution has a concentration of 30% and a volume of 14 liters. To find the amount of acid in the resulting solution, we can multiply the concentration by the volume.
acid_in_resulting_solution = 0.3 * 14
print(acid_in_resulting_solution)
Step 3: Set Up an Equation
Let x be the amount of acid in Solution 1. Since the resulting solution is a mixture of Solution 1 and Solution 2, we can set up an equation based on the amount of acid in each solution.
x + 4 = 0.3 * 14
Step 4: Solve for x
To solve for x, we can subtract 4 from both sides of the equation.
x = 0.3 * 14 - 4
print(x)
In this article, we have solved a problem involving the mixing of two acid solutions, resulting in a 30% acid solution. We have used the concept of mixture and percentage to calculate the amount of acid in each solution. The resulting solution has a concentration of 30% and a volume of 14 liters. We have also set up an equation based on the amount of acid in each solution and solved for x, the amount of acid in Solution 1.
This problem is a classic example of a mixture and percentage problem. It requires the student to understand the concept of mixture and percentage and to apply it to a real-world scenario. The problem also requires the student to set up an equation and solve for a variable, which is an important skill in chemistry.
This problem has real-world applications in various fields, including chemistry, biology, and environmental science. In chemistry, mixtures and solutions are used in various experiments and processes, such as titration and chromatography. In biology, mixtures and solutions are used in various experiments and processes, such as cell culture and DNA extraction. In environmental science, mixtures and solutions are used in various experiments and processes, such as water treatment and pollution monitoring.
In conclusion, this problem is a great example of a mixture and percentage problem. It requires the student to understand the concept of mixture and percentage and to apply it to a real-world scenario. The problem also requires the student to set up an equation and solve for a variable, which is an important skill in chemistry. We hope that this article has provided a clear and concise solution to the problem and has helped the student to understand the concept of mixture and percentage.
A Chemist's Acid Solution Conundrum: A Problem of Mixture and Percentage - Q&A
In our previous article, we solved a problem involving the mixing of two acid solutions, resulting in a 30% acid solution. We used the concept of mixture and percentage to calculate the amount of acid in each solution. In this article, we will provide a Q&A section to help students and professionals understand the concept of mixture and percentage and to apply it to real-world scenarios.
Q: What is a mixture and percentage problem?
A: A mixture and percentage problem is a type of problem that involves the mixing of two or more solutions with different concentrations. The resulting solution will have a concentration that is a weighted average of the concentrations of the two original solutions.
Q: How do I solve a mixture and percentage problem?
A: To solve a mixture and percentage problem, you need to follow these steps:
- Identify the concentrations of the two original solutions.
- Identify the volume of each solution.
- Calculate the amount of acid in each solution.
- Set up an equation based on the amount of acid in each solution.
- Solve for the variable.
Q: What is the difference between a mixture and a solution?
A: A mixture is a physical combination of two or more substances, while a solution is a homogeneous mixture of two or more substances.
Q: How do I calculate the amount of acid in a solution?
A: To calculate the amount of acid in a solution, you need to multiply the concentration of the solution by the volume of the solution.
Q: What is the concept of weighted average?
A: The concept of weighted average is a mathematical concept that involves calculating the average of two or more values, where each value is weighted by its proportion of the total.
Q: How do I apply the concept of mixture and percentage to real-world scenarios?
A: The concept of mixture and percentage is widely used in various fields, including chemistry, biology, and environmental science. In chemistry, mixtures and solutions are used in various experiments and processes, such as titration and chromatography. In biology, mixtures and solutions are used in various experiments and processes, such as cell culture and DNA extraction. In environmental science, mixtures and solutions are used in various experiments and processes, such as water treatment and pollution monitoring.
Q: How is the concept of mixture and percentage used in chemistry?
A: The concept of mixture and percentage is widely used in chemistry to calculate the concentration of a solution. It is also used to determine the amount of a substance in a solution.
Q: How is the concept of mixture and percentage used in biology?
A: The concept of mixture and percentage is used in biology to calculate the concentration of a solution. It is also used to determine the amount of a substance in a solution.
Q: How is the concept of mixture and percentage used in environmental science?
A: The concept of mixture and percentage is used in environmental science to calculate the concentration of a solution. It is also used to determine the amount of a substance in a solution.
In conclusion, the concept of mixture and percentage is a fundamental concept in chemistry, biology, and environmental science. It is widely used to calculate the concentration of a solution and to determine the amount of a substance in a solution. We hope that this Q&A article has provided a clear and concise explanation of the concept of mixture and percentage and has helped students and professionals to understand and apply it to real-world scenarios.