Grant Plans To Evaporate Enough Water From 22 Gallons Of A $16%$ Ammonia Solution To Make A $24%$ Ammonia Solution. Which Equation Can He Use To Find $ N N N [/tex], The Number Of Gallons Of Water He Should Remove?A.

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Introduction

Grant is faced with a problem in chemistry where he needs to evaporate a certain amount of water from a 16% ammonia solution to create a 24% ammonia solution. This problem requires Grant to use the concept of concentration and the amount of substance to find the number of gallons of water he should remove. In this article, we will explore the equation that Grant can use to solve this problem.

Understanding the Problem

Grant starts with 22 gallons of a 16% ammonia solution. This means that 16% of the solution is ammonia, and the remaining 84% is water. Grant wants to evaporate enough water to make a 24% ammonia solution. This means that the amount of ammonia remains the same, but the amount of water decreases, resulting in a higher concentration of ammonia.

The Concept of Concentration

Concentration is a measure of the amount of substance (in this case, ammonia) per unit volume of a solution. It is usually expressed as a percentage or a ratio. In this problem, the concentration of ammonia in the initial solution is 16%, and the concentration of ammonia in the final solution is 24%.

The Equation for Finding the Number of Gallons of Water to Remove

Let's denote the number of gallons of water to remove as n. The amount of ammonia in the initial solution is 16% of 22 gallons, which is 0.16 x 22 = 3.52 gallons. The amount of ammonia in the final solution is 24% of (22 - n) gallons, which is 0.24 x (22 - n).

Since the amount of ammonia remains the same, we can set up the following equation:

0.16 x 22 = 0.24 x (22 - n)

Simplifying the equation, we get:

3.52 = 5.28 - 0.24n

Subtracting 5.28 from both sides, we get:

-1.76 = -0.24n

Dividing both sides by -0.24, we get:

n = 7.33

Therefore, Grant should remove approximately 7.33 gallons of water to make a 24% ammonia solution.

Conclusion

Grant's problem is a classic example of a concentration problem in chemistry. By using the concept of concentration and the amount of substance, Grant can find the number of gallons of water he should remove to make a 24% ammonia solution. The equation that Grant can use to solve this problem is:

0.16 x 22 = 0.24 x (22 - n)

This equation can be simplified to:

n = 7.33

Grant should remove approximately 7.33 gallons of water to make a 24% ammonia solution.

Discussion

This problem is a great example of how chemistry can be applied to real-world situations. Grant's problem requires him to think critically and use mathematical equations to solve a practical problem. This type of problem is commonly encountered in industries such as pharmaceuticals, food processing, and water treatment, where the concentration of substances is critical to the quality and safety of the final product.

Key Takeaways

  • Concentration is a measure of the amount of substance per unit volume of a solution.
  • The amount of substance remains the same in a concentration problem.
  • The equation for finding the number of gallons of water to remove is:

0.16 x 22 = 0.24 x (22 - n)

This equation can be simplified to:

n = 7.33

Grant should remove approximately 7.33 gallons of water to make a 24% ammonia solution.

References

  • Chemistry: An Atoms First Approach, by Steven S. Zumdahl
  • General Chemistry: Principles and Modern Applications, by Linus Pauling

Introduction

In our previous article, we explored the problem of Grant evaporating a certain amount of water from a 16% ammonia solution to create a 24% ammonia solution. We derived the equation that Grant can use to find the number of gallons of water he should remove. In this article, we will answer some common questions related to this problem.

Q: What is the initial concentration of ammonia in the solution?

A: The initial concentration of ammonia in the solution is 16%. This means that 16% of the solution is ammonia, and the remaining 84% is water.

Q: What is the final concentration of ammonia in the solution?

A: The final concentration of ammonia in the solution is 24%. This means that 24% of the solution is ammonia, and the remaining 76% is water.

Q: What is the amount of ammonia in the initial solution?

A: The amount of ammonia in the initial solution is 3.52 gallons. This is calculated by multiplying the initial concentration of ammonia (16%) by the initial volume of the solution (22 gallons).

Q: What is the amount of ammonia in the final solution?

A: The amount of ammonia in the final solution is 5.28 gallons. This is calculated by multiplying the final concentration of ammonia (24%) by the final volume of the solution (22 - n gallons).

Q: How do we find the number of gallons of water to remove?

A: We find the number of gallons of water to remove by setting up an equation based on the amount of ammonia in the initial and final solutions. The equation is:

0.16 x 22 = 0.24 x (22 - n)

Simplifying the equation, we get:

n = 7.33

Q: What if the initial volume of the solution is not 22 gallons?

A: If the initial volume of the solution is not 22 gallons, we need to adjust the equation accordingly. The amount of ammonia in the initial solution is still 16% of the initial volume, and the amount of ammonia in the final solution is still 24% of the final volume.

Q: What if the final concentration of ammonia is not 24%?

A: If the final concentration of ammonia is not 24%, we need to adjust the equation accordingly. The amount of ammonia in the final solution is still 24% of the final volume, but the amount of ammonia in the initial solution will be different.

Q: Can we use this equation for other concentration problems?

A: Yes, we can use this equation for other concentration problems. The equation is based on the concept of concentration and the amount of substance, which is applicable to any concentration problem.

Conclusion

Grant's ammonia solution problem is a classic example of a concentration problem in chemistry. By using the concept of concentration and the amount of substance, we can find the number of gallons of water to remove to make a 24% ammonia solution. The equation that we derived can be used for other concentration problems, making it a useful tool in chemistry and related fields.

Key Takeaways

  • The initial concentration of ammonia in the solution is 16%.
  • The final concentration of ammonia in the solution is 24%.
  • The amount of ammonia in the initial solution is 3.52 gallons.
  • The amount of ammonia in the final solution is 5.28 gallons.
  • The equation for finding the number of gallons of water to remove is:

0.16 x 22 = 0.24 x (22 - n)

This equation can be simplified to:

n = 7.33

Grant should remove approximately 7.33 gallons of water to make a 24% ammonia solution.

References

  • Chemistry: An Atoms First Approach, by Steven S. Zumdahl
  • General Chemistry: Principles and Modern Applications, by Linus Pauling

Note: The references provided are for general chemistry textbooks and are not specific to this problem. However, they provide a good starting point for further reading and understanding of the concepts involved in this problem.