To calculate the volume of a sample of alcohol in liters, given its mass in grams and the density in pounds per gallon, we'll follow these steps:

Step 1: Convert the mass from grams to pounds

First, we need to convert the mass of alcohol from grams to pounds. The conversion factor is: $1 \, \text{pound (lb)} = 453.592 \, \text{grams (g)}$ So, the mass in pounds is: $\text{Mass in pounds} = \frac{1587.57 \, \text{g}}{453.592 \, \text{g/lb}}$

Step 2: Calculate the volume in gallons

Using the formula for density, $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$, we can rearrange it to solve for the volume: $\text{Volume in gallons} = \frac{\text{Mass in pounds}}{\text{Density in lb/gal}}$

Step 3: Convert gallons to liters

To convert gallons to liters, use the conversion factor: $1 \, \text{gallon} = 3.78541 \, \text{liters}$ Thus, the final step is: $\text{Volume in liters} = \text{Volume in gallons} \times 3.78541$

Now let's compute this step-by-step.The volume of the alcohol sample is approximately 2.01 liters.

Would you like further details or have any questions?

Here are 5 related questions you might explore:

1. How does the volume change if the density of the alcohol decreases?
2. How would you calculate the volume if the mass were given in kilograms?
3. What is the relationship between mass, volume, and density in other substances?
4. How can you find the density of a liquid if you're given its mass and volume?
5. What are the practical applications of density in industries such as pharmaceuticals?

Tip: When working with units in physics or chemistry, always ensure all quantities are in compatible units before performing calculations.