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 solve these problems, we need to use the formula that relates mass, volume, and density:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
We can rearrange this formula to solve for either mass or volume:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
Part 1: Find the volume of 145.1 g of Germanium (Ge)
We know:
- Density of Ge = 5.323 g/mL
- Mass = 145.1 g
Now, to find the volume:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{145.1 \, \text{g}}{5.323 \, \text{g/mL}}
]
[
\text{Volume} = 27.3 \, \text{mL}
]
So, the volume of 145.1 g of Ge is 27.3 mL to the nearest 0.01 mL.
Part 2: Find the mass of 15.4 mL of Germanium (Ge)
We know:
- Density of Ge = 5.323 g/mL
- Volume = 15.4 mL
Now, to find the mass:
[
\text{Mass} = \text{Density} \times \text{Volume} = 5.323 \, \text{g/mL} \times 15.4 \, \text{mL}
]
[
\text{Mass} = 82.0 \, \text{g}
]
So, the mass of 15.4 mL of Ge is 82.000 g to the nearest 0.001 g.
Explanation:
Density is a physical property that describes how much mass is contained in a given volume. It is typically expressed in units of grams per milliliter (g/mL). By knowing the density, we can use the formula to calculate either the volume or mass of a substance when the other is provided.
In the first part, we used the rearranged formula ( \text{Volume} = \frac{\text{Mass}}{\text{Density}} ) to calculate the volume from the given mass and density. In the second part, we used the formula ( \text{Mass} = \text{Density} \times \text{Volume} ) to calculate the mass from the given volume and density.
Here is the bar chart representing the calculated volume and mass for Germanium (Ge). The first bar represents the volume of 145.1 g of Ge, which is 27.3 mL, and the second bar represents the mass of 15.4 mL of Ge, which is 82.000 g.
The calculations are based on the density formula, and the chart helps visually demonstrate the relationship between mass, volume, and density for Germanium.