To find the order of mass from least to greatest, we need to calculate the mass of the gas in each container. The mass of a gas can be calculated using the formula:
[tex]\[ \text{Mass} = \text{Density} \times \text{Volume} \][/tex]
Here are the steps for each container:
### Container A: Hydrogen
#### Step 1: Calculate the volume of the cube.
- The volume [tex]\( V \)[/tex] of a cube is given by:
[tex]\[ V = \text{side}^3 \][/tex]
- For Container A, the side length is 15 cm:
[tex]\[ V = 15^3 = 3375 \, \text{cm}^3 \][/tex]
#### Step 2: Calculate the mass.
- The density of Hydrogen is 0.09 mg/cm³:
[tex]\[ \text{Mass} = 0.09 \, \text{mg/cm}^3 \times 3375 \, \text{cm}^3 = 303.75 \, \text{mg} \][/tex]
### Container B: Helium
#### Step 1: Calculate the volume of the rectangular prism.
- The volume [tex]\( V \)[/tex] of a rectangular prism is given by:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
- For Container B, the dimensions are 14 cm, 12 cm, and 10 cm:
[tex]\[ V = 14 \times 12 \times 10 = 1680 \, \text{cm}^3 \][/tex]
#### Step 2: Calculate the mass.
- The density of Helium is 0.175 mg/cm³:
[tex]\[ \text{Mass} = 0.175 \, \text{mg/cm}^3 \times 1680 \, \text{cm}^3 = 294 \, \text{mg} \][/tex]
### Container C: Nitrogen
#### Step 1: Calculate the volume of the sphere.
- The volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi \text{radius}^3 \][/tex]
- For Container C, the diameter is 8 cm, so the radius is:
[tex]\[ \text{Radius} = \frac{8}{2} = 4 \, \text{cm} \][/tex]
- Plugging in the radius:
[tex]\[ V = \frac{4}{3} \pi (4)^3 \approx \frac{4}{3} \pi (64) \approx 268.08 \, \text{cm}^3 \][/tex]
#### Step 2: Calculate the mass.
- The density of Nitrogen is 1.251 mg/cm³:
[tex]\[ \text{Mass} = 1.251 \, \text{mg/cm}^3 \times 268.08 \, \text{cm}^3 \approx 335.37 \, \text{mg} \][/tex]
### Order from Least to Greatest Mass
- Container B: 294.0 mg
- Container A: 303.75 mg
- Container C: 335.37 mg
Therefore, the correct order of mass from least to greatest is:
[tex]\[ \text{B, A, C} \][/tex]
