The density of germanium (Ge) is 5.323 g/mL. Enter the volume value in units of mL to the nearest 0.01 mL and include the unit. Enter mass value in units of grams to the nearest 0.001 g and include the unit. The volume of 145.1 g of Ge to the nearest 0.01 mL is Number Units. The mass of 15.4 mL of Ge to the nearest 0.001 g is Number Units.
The correct answer and explanation is :
To calculate both the volume and mass of Germanium (Ge) given its density, we can use the formula for density:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Where:
- Density of Germanium (Ge) = 5.323 g/mL
- Mass is in grams (g)
- Volume is in milliliters (mL)
1. Volume Calculation for 145.1 g of Ge:
The formula can be rearranged to calculate the volume:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
Substituting the given values:
[
\text{Volume} = \frac{145.1 \, \text{g}}{5.323 \, \text{g/mL}} \approx 27.3 \, \text{mL}
]
So, the volume of 145.1 g of Ge is approximately 27.30 mL (rounded to the nearest 0.01 mL).
2. Mass Calculation for 15.4 mL of Ge:
Now, we use the same density formula to calculate the mass for a given volume. We rearrange the density formula to solve for mass:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
Substituting the given values:
[
\text{Mass} = 5.323 \, \text{g/mL} \times 15.4 \, \text{mL} \approx 82.0 \, \text{g}
]
So, the mass of 15.4 mL of Ge is approximately 82.000 g (rounded to the nearest 0.001 g).
Summary of Results:
- The volume of 145.1 g of Ge is 27.30 mL.
- The mass of 15.4 mL of Ge is 82.000 g.
Explanation:
Density is a physical property that represents how much mass is contained in a given volume. In this case, the density of Germanium is provided as 5.323 g/mL. Using the formula for density, we can easily calculate either the mass or volume when one is known.
The first part of the question asks for the volume of a known mass (145.1 g). By dividing the mass by the density, we calculate the volume. The second part asks for the mass of a known volume (15.4 mL). By multiplying the volume by the density, we calculate the mass.
Both of these calculations follow basic principles of density, and the results have been rounded according to the required significant figures.