A liquid in the lab has a density of 1.17 g/cm3. What is the volume in liters of 3.02 kg of the liquid? Demonstrate each conversion factor.
The Correct Answer and Explanation is:
To solve this problem, we need to convert the mass of the liquid from kilograms to grams, then use the density formula to find the volume, and finally convert the volume from cubic centimeters (cm³) to liters (L).
Step 1: Convert mass from kilograms to grams
The mass given is 3.02 kg, and we know that 1 kg is equal to 1000 grams. Therefore:3.02 kg×1000 g1 kg=3020 g3.02 \, \text{kg} \times \frac{1000 \, \text{g}}{1 \, \text{kg}} = 3020 \, \text{g}3.02kg×1kg1000g=3020g
So, the mass of the liquid is 3020 grams.
Step 2: Use the density formula to find the volume
The formula for density is:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
We can rearrange this formula to solve for volume:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
Given:
- Mass = 3020 g
- Density = 1.17 g/cm³
Now, substitute these values into the equation:Volume=3020 g1.17 g/cm3=2573.50 cm3\text{Volume} = \frac{3020 \, \text{g}}{1.17 \, \text{g/cm}^3} = 2573.50 \, \text{cm}^3Volume=1.17g/cm33020g=2573.50cm3
So, the volume of the liquid is 2573.50 cubic centimeters (cm³).
Step 3: Convert volume from cubic centimeters to liters
1 liter is equal to 1000 cubic centimeters (cm³). Therefore, to convert cm³ to liters, we use the conversion factor:Volume in liters=2573.50 cm31000 cm3/L=2.5735 L\text{Volume in liters} = \frac{2573.50 \, \text{cm}^3}{1000 \, \text{cm}^3/\text{L}} = 2.5735 \, \text{L}Volume in liters=1000cm3/L2573.50cm3=2.5735L
Final Answer:
The volume of the liquid is 2.5735 liters.
This method uses unit conversions and density to find the desired result, ensuring that all units are consistent and correctly converted.
