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2. A sample of oil has a density of [tex]0.85 \, \text{g/mL}[/tex]. What is the mass of 3.00 barrels of oil in kilograms if a barrel of oil is 42.0 gallons? [1 gallon [tex]=3.8754 \, \text{L}[/tex]]

A. 313 kg
B. 415 kg
C. 488 kg

Sagot :

GinnyAnsweridn
To determine the mass of 3.00 barrels of oil in kilograms, we will follow several steps involving unit conversions and density calculations.

### Step-by-Step Solution:

1. Determine the volume of oil in barrels:
Given:
- Number of barrels = 3.00 barrels
- Volume per barrel = 42.0 gallons

Therefore, the total volume in gallons is:
[tex]\( 3.00 \times 42.0 = 126.0 \)[/tex] gallons

2. Convert the volume of oil from gallons to liters:
Using the conversion factor:
- 1 gallon = 3.8754 liters

The total volume in liters is:
[tex]\( 126.0 \times 3.8754 = 488.3004 \)[/tex] liters

3. Convert the volume from liters to milliliters:
- 1 liter = 1000 milliliters

The total volume in milliliters is:
[tex]\( 488.3004 \times 1000 = 488300.4 \)[/tex] milliliters

4. Calculate the mass of the oil in grams:
Given:
- Density of oil = [tex]\( 0.85 \)[/tex] g/mL

The mass in grams is:
[tex]\( 0.85 \times 488300.4 = 415055.34 \)[/tex] grams

5. Convert the mass from grams to kilograms:
- 1 kilogram = 1000 grams

The mass in kilograms is:
[tex]\( \frac{415055.34}{1000} = 415.05534 \)[/tex] kilograms

### Final Result:
The mass of 3.00 barrels of oil is approximately 415 kilograms.

Hence, the correct answer is B. 415 kg.
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