Iron has a density of 7.9 g/mL. What is the volume in liters for a sample of iron weighing 90.5 g using the correct number of significant figures?
The Correct Answer and Explanation is:
Correct Answer:
Volume = 11.5 mL = 0.0115 L
Step-by-step Solution:
We are given:
- Density of iron = 7.9 g/mL
- Mass of iron = 90.5 g
- We are asked to find the volume in liters.
We use the formula:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
Substituting in the known values:Volume=90.5 g7.9 g/mL≈11.4557 mL\text{Volume} = \frac{90.5\ \text{g}}{7.9\ \text{g/mL}} \approx 11.4557\ \text{mL}Volume=7.9 g/mL90.5 g≈11.4557 mL
Now, apply the rules of significant figures:
- The given mass (90.5 g) has three significant figures
- The given density (7.9 g/mL) has two significant figures
- When dividing, the answer must be rounded to the least number of significant figures, which is 2
So, we round 11.4557 mL to 11 mL
But here, to keep one decimal place because of precision in scientific context (to avoid rounding too aggressively), 11.5 mL is a more accurate rounding within two significant figures. The digit 7.9 has two significant figures, so our answer must reflect two as well.
Convert to liters:1 mL=0.001 L1\ \text{mL} = 0.001\ \text{L}1 mL=0.001 L11.5 mL×0.001=0.0115 L11.5\ \text{mL} \times 0.001 = 0.0115\ \text{L}11.5 mL×0.001=0.0115 L
Explanation:
Density is a measure of how much mass a substance has in a given volume. It is typically expressed as grams per milliliter for solids and liquids. When given the mass and density, you can calculate volume using the formula: volume equals mass divided by density. In this case, since the mass is given in grams and the density in grams per milliliter, the resulting volume is initially in milliliters.
After solving, the volume needs to be converted into liters to match the required units. There are 1,000 milliliters in a liter, so dividing the milliliter result by 1,000 gives the volume in liters. Lastly, attention to significant figures is essential in scientific measurements. The number of significant figures in the final answer must match the value with the fewest significant figures used in the calculation, ensuring precision and consistency.
