The density of water at room temperature (25 degrees C) is 0.9970 g cm-3. How many pounds does the water in a full 5.0 gallon pail weigh?
The Correct Answer and Explanation is:
To find how many pounds the water in a full 5.0-gallon pail weighs at 25°C (where the density of water is 0.9970 g/cm³), we must go through a unit conversion process:
✅ Correct Answer: Approximately 41.6 pounds
Step-by-Step Explanation (300+ words):
This problem involves converting volume to mass and then converting mass from grams to pounds. We’ll break this down into steps:
1. Convert Gallons to Cubic Centimeters (cm³)
We know:
- 1 US gallon = 3.78541 liters
- 1 liter = 1,000 cm³
So:
$$
5.0 \text{ gallons} = 5.0 \times 3.78541 = 18.92705 \text{ liters}
$$
$$
18.92705 \text{ liters} = 18.92705 \times 1000 = 18,927.05 \text{ cm}^3
$$
2. Use the Density to Calculate Mass in Grams
Density of water at 25°C = 0.9970 g/cm³
$$
\text{Mass} = \text{Volume} \times \text{Density}
$$
$$
\text{Mass} = 18,927.05 \text{ cm}^3 \times 0.9970 \text{ g/cm}^3 = 18,869.27 \text{ grams}
$$
3. Convert Grams to Pounds
We know:
- 1 pound (lb) = 453.59237 grams
$$
\text{Mass in pounds} = \frac{18,869.27}{453.59237} \approx 41.6 \text{ pounds}
$$
✔ Summary:
- You started with 5.0 gallons of water.
- Converted gallons to cm³ to match the units of density.
- Used the density to find mass in grams.
- Finally, converted grams to pounds.
This method emphasizes the importance of proper unit conversion in solving real-world science problems. A slight difference in the density (for example, if water were warmer or colder) would have a small effect on the final weight. But at room temperature (25°C), water is nearly at its maximum density, which helps standardize calculation