A technical machinist is asked to build a cubical steel tank that will hold 230L of water

A technical machinist is asked to build a cubical steel tank that will hold 230L of water.
Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001m.

What is the molecular geometry of SF₄O?

a. trigonal bipyramidal

b. pentagonal

c. square pyramidal

d. tetrahedral

e. trigonal planar

The Correct Answer and Explanation is :

Problem 1: Smallest Possible Inside Length of the Tank

We need to determine the smallest possible inside length (( l )) of a cubical steel tank that can hold 230 liters of water.

Step 1: Convert Liters to Cubic Meters

Since ( 1 ) liter ( = 0.001 ) cubic meters, we convert:

[
230L = 230 \times 0.001 = 0.230 \text{ m}^3
]

Step 2: Use the Volume Formula for a Cube

The volume of a cube is given by:

[
V = l^3
]

Setting ( V = 0.230 ) m³:

[
l^3 = 0.230
]

Step 3: Solve for ( l )

Taking the cube root:

[
l = \sqrt[3]{0.230}
]

Using a calculator:

[
l \approx 0.608
]

Step 4: Round to the Nearest 0.001m

[
l \approx 0.608 \text{ m}
]

Final Answer: 0.608 m

Problem 2: Molecular Geometry of SF₄O

Correct Answer: (a) Trigonal Bipyramidal

Explanation:

Valence Electrons & Lewis Structure

Sulfur (S): 6 valence electrons
Fluorine (F) (×4): ( 4 \times 7 = 28 ) valence electrons
Oxygen (O): 6 valence electrons
Total Electrons: ( 6 + 28 + 6 = 40 ) valence electrons The sulfur atom is the central atom with four fluorine atoms and one oxygen atom bonded to it.

Electron Domain & Molecular Shape

Steric Number (SN) Calculation:
The steric number is determined by bonded atoms + lone pairs around the central atom.
- 4 fluorine atoms + 1 oxygen atom → 5 regions
- No lone pairs on sulfur
A steric number of 5 corresponds to a trigonal bipyramidal electronic geometry.

Molecular Geometry

Since all five positions are occupied by atoms, the molecular shape remains trigonal bipyramidal.
If there were lone pairs on sulfur, the shape would have been distorted.

Comparison with Other Options

Square Pyramidal (c): Requires 6 electron groups (not applicable).
Tetrahedral (d): Requires 4 electron groups (not applicable).
Trigonal Planar (e): Requires 3 electron groups (not applicable).
Pentagonal (b): Requires 6+ electron groups (not applicable).

Conclusion:

The correct molecular geometry of SF₄O is Trigonal Bipyramidal (option a).