To solve this question, we need to determine the mass of the gas contained in each container by using the respective densities and volumes of the containers.
### Step 1: Calculate the volume of each container
Container A (Cube):
- Side length = 15 cm
- Volume = side³ = [tex]\(15^3\)[/tex] = [tex]\(3375 \, cm^3\)[/tex]
Container B (Rectangular Prism):
- Dimensions = 14 cm, 12 cm, 10 cm
- Volume = length × width × height = [tex]\(14 \times 12 \times 10 = 1680 \, cm^3 \)[/tex]
Container C (Sphere):
- Diameter = 8 cm, so the radius = 4 cm
- Volume = [tex]\(\frac{4}{3} \pi \times \text{radius}^3 = \frac{4}{3} \pi \times 4^3\)[/tex] = [tex]\(\frac{4}{3} \pi \times 64 \approx 268.08 \, cm^3 \)[/tex]
### Step 2: Use the volume and density to find the mass of gases in each container
Container A (Hydrogen):
- Density = 0.09 mg/cm³
- Mass = Density × Volume = [tex]\(0.09 \, mg/cm^3 \times 3375 \, cm^3 = 303.75 \, mg \)[/tex]
Container B (Helium):
- Density = 0.175 mg/cm³
- Mass = Density × Volume = [tex]\(0.175 \, mg/cm^3 \times 1680 \, cm^3 = 294 \, mg \)[/tex]
Container C (Nitrogen):
- Density = 1.251 mg/cm³
- Mass = Density × Volume = [tex]\(1.251 \, mg/cm^3 \times 268.08 \, cm^3 \approx 335.37 \, mg \)[/tex]
### Step 3: Order the masses from least to greatest
The masses of the gases are:
- Container A (Hydrogen): 303.75 mg
- Container B (Helium): 294 mg
- Container C (Nitrogen): 335.37 mg
So, the correct order of the masses from least to greatest is:
[tex]\[
B \, (294 \, mg) < A \, (303.75 \, mg) < C \, (335.37 \, mg)
\][/tex]
Therefore, the correct order is:
[tex]\[ B \, < \, A \, < \, C \][/tex]
