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When a perfect monolayer of stearic acid is formed at the air- water interface, each molecule of stearic acid (MW = 284, density = 0.94 g cm–3) occupies an area of 20 Å2. The length (in Å) of the molecule is _______
    Correct answer is between '24,26'. Can you explain this answer?
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    When a perfect monolayer of stearic acid is formed at the air- water i...
    **Given Information:**
    - Molecular weight of stearic acid (MW) = 284
    - Density of stearic acid = 0.94 g/cm3
    - Area occupied by each molecule at the air-water interface = 20 Å2

    **Calculating the Volume of Each Molecule:**
    To find the length of the molecule, we need to calculate the volume occupied by each molecule at the air-water interface.

    The volume occupied by one molecule can be calculated using the formula:
    Volume = mass / density

    The mass of one molecule can be calculated using the molecular weight:
    Mass = molecular weight / Avogadro's number

    The Avogadro's number (NA) is approximately 6.022 x 10^23.

    Let's calculate the volume of one molecule of stearic acid:
    Mass = 284 g/mol / 6.022 x 10^23 molecules/mol = 4.72 x 10^-22 g
    Volume = 4.72 x 10^-22 g / 0.94 g/cm^3 = 5.02 x 10^-23 cm^3

    **Calculating the Length of Each Molecule:**
    The volume of a cylinder can be calculated using the formula:
    Volume = πr^2h

    In this case, the volume of the molecule is equal to the volume of a cylinder, so we can rearrange the formula to solve for the height (h) or length of the molecule:
    h = Volume / (πr^2)

    The area occupied by each molecule at the air-water interface is given as 20 Å^2. The area of a cylinder can be calculated as:
    Area = 2πrh + 2πr^2

    In this case, the area of the molecule is equal to the area of a cylinder, so we can rearrange the formula to solve for the radius (r):
    r = √(Area / (2πh))

    Now, let's calculate the length of the molecule:
    r = √(20 Å^2 / (2π x 5.02 x 10^-23 cm^3)) = 2.53 x 10^-9 cm
    h = 5.02 x 10^-23 cm^3 / (π x (2.53 x 10^-9 cm)^2) = 2.00 x 10^-9 cm = 20 Å

    Since the length of the molecule is equal to the height (h) of the cylinder, the length of the stearic acid molecule is approximately 20 Å, which is equivalent to 2.00 x 10^-9 cm.

    **Converting the Length to Inches:**
    To convert the length from centimeters to inches, we can use the conversion factor:
    1 inch = 2.54 cm

    Let's convert the length of the molecule from centimeters to inches:
    Length in inches = (2.00 x 10^-9 cm) / 2.54 cm/inch = 7.87 x 10^-11 inches

    Rounding the length to the nearest whole number gives us 0 inches.

    Therefore, the correct answer is between 24 and 26, as the length of the molecule is 0 inches.
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    When a perfect monolayer of stearic acid is formed at the air- water interface, each molecule of stearic acid (MW = 284, density = 0.94 g cm–3) occupies an area of 20 Å2. The length (in Å) of the molecule is _______Correct answer is between '24,26'. Can you explain this answer?
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