Mass of alcohol in one bottle

Oct 13, 2025 by wbrum.org 47 views

Understanding the Problem

To solve this problem, we need to calculate the total amount of alcohol in 180 bottles of a mouthwash. We are given the percentage of alcohol in the mouthwash, the volume of each bottle in pints, and the density of the mouthwash in g/ml.

Calculating the Volume of Alcohol in One Bottle

First, we need to convert the volume of one bottle from pints to milliliters. We know that 1 pint is equal to 473.176 milliliters. Therefore, the volume of one bottle in milliliters is:

0.358 pints * 473.176 milliliters/pint = 169.9 milliliters

Calculating the Mass of One Bottle

Next, we need to calculate the mass of one bottle in grams. We are given the density of the mouthwash as 0.876 g/ml. Therefore, the mass of one bottle in grams is:

169.9 milliliters * 0.876 g/ml = 149.1 grams

Calculating the Mass of Alcohol in One Bottle

Now, we need to calculate the mass of alcohol in one bottle. We are given that the mouthwash contains 21.6% alcohol by mass. Therefore, the mass of alcohol in one bottle is:

149.1 grams * 0.216 = 32.2 grams

Calculating the Total Mass of Alcohol in 180 Bottles

Finally, we need to calculate the total mass of alcohol in 180 bottles. We can do this by multiplying the mass of alcohol in one bottle by 180:

32.2 grams/bottle * 180 bottles = 5780 grams

Converting the Total Mass of Alcohol to Kilograms

To convert the total mass of alcohol from grams to kilograms, we can divide by 1000:

5780 grams / 1000 = 5.78 kilograms

Conclusion

In conclusion, there are approximately 5.78 kilograms of alcohol in 180 bottles of the oral rinse.

Additional Information

Density of the mouthwash: 0.876 g/ml
Percentage of alcohol: 21.6%
Volume of one bottle: 0.358 pints
Mass of one bottle: 149.1 grams
Mass of alcohol in one bottle: 32.2 grams
Total mass of alcohol in 180 bottles: 5780 grams
Total mass of alcohol in 180 bottles (in kilograms): 5.78 kilograms

Understanding the Problem

Q&A

Q: What is the percentage of alcohol in the mouthwash?

A: The mouthwash contains 21.6% alcohol by mass.

Q: What is the volume of one bottle in milliliters?

A: The volume of one bottle in milliliters is 169.9 milliliters.

Q: What is the mass of one bottle in grams?

A: The mass of one bottle in grams is 149.1 grams.

Q: What is the mass of alcohol in one bottle?

A: The mass of alcohol in one bottle is 32.2 grams.

Q: How many kilograms of alcohol are in 180 bottles of the oral rinse?

A: There are approximately 5.78 kilograms of alcohol in 180 bottles of the oral rinse.

Q: What is the density of the mouthwash?

A: The density of the mouthwash is 0.876 g/ml.

Q: What is the volume of one bottle in pints?

A: The volume of one bottle in pints is 0.358 pints.

Q: How can I convert the total mass of alcohol from grams to kilograms?

A: To convert the total mass of alcohol from grams to kilograms, you can divide by 1000.

Q: What is the total mass of alcohol in 180 bottles in grams?

A: The total mass of alcohol in 180 bottles is 5780 grams.

Q: What is the total mass of alcohol in 180 bottles in kilograms?

A: The total mass of alcohol in 180 bottles is 5.78 kilograms.

Additional Information

Density of the mouthwash: 0.876 g/ml
Percentage of alcohol: 21.6%
Volume of one bottle: 0.358 pints
Mass of one bottle: 149.1 grams
Mass of alcohol in one bottle: 32.2 grams
Total mass of alcohol in 180 bottles: 5780 grams
Total mass of alcohol in 180 bottles (in kilograms): 5.78 kilograms

Real-World Applications

Calculating the amount of alcohol in a mouthwash can be useful in various industries, such as pharmaceuticals, cosmetics, and food and beverage.
Understanding the density and percentage of alcohol in a product can help manufacturers create more accurate labels and packaging.
Calculating the total mass of alcohol in a product can also help consumers make informed decisions about their purchases.

Conclusion

In conclusion, calculating the amount of alcohol in a mouthwash requires understanding the density and percentage of alcohol in the product, as well as the volume of each bottle. By following these steps, you can accurately calculate the total mass of alcohol in 180 bottles of the oral rinse.