1 g of activated charcoal has a surface area 103 m3. If complete monolayer coverage is assumed, how much NH3 in cm3 at STP would be adsorbed on the surface of 25 g of the charcoal. Given diameter of NH3 molecule = 0.3 nmCorrect answer is '13.168'. Can you explain this answer?

Question

Answer

To solve this problem, we need to calculate the amount of NH3 that can be adsorbed on the surface of the activated charcoal.

Step 1: Calculate the surface area of the charcoal in cm2

Given:
- Surface area of 1 g of activated charcoal = 103 m2 = 103 × 104 cm2 (1 m2 = 104 cm2)
- Mass of activated charcoal = 25 g

The surface area of 25 g of activated charcoal can be calculated as follows:

Surface area of charcoal = Surface area of 1 g charcoal × Mass of charcoal
Surface area of charcoal = 103 × 104 cm2/g × 25 g
Surface area of charcoal = 25 × 103 × 104 cm2
Surface area of charcoal = 2.5 × 105 × 104 cm2
Surface area of charcoal = 2.5 × 109 cm2

Step 2: Calculate the number of NH3 molecules that can be adsorbed on the surface of the charcoal

Given:
- Diameter of NH3 molecule = 0.3 nm = 0.3 × 10-7 cm (1 nm = 10-7 cm)

Since we are assuming complete monolayer coverage, the number of NH3 molecules that can be adsorbed on the surface of the charcoal can be calculated using the formula:

Number of NH3 molecules = Surface area of charcoal / Area occupied by one NH3 molecule

Area occupied by one NH3 molecule can be calculated using the formula for the area of a circle:

Area occupied by one NH3 molecule = π × (diameter/2)2
Area occupied by one NH3 molecule = π × (0.3 × 10-7 cm/2)2
Area occupied by one NH3 molecule = π × (0.15 × 10-7 cm)2
Area occupied by one NH3 molecule = π × 2.25 × 10-14 cm2
Area occupied by one NH3 molecule = 7.07 × 10-14 cm2 (taking π = 3.14)

Number of NH3 molecules = 2.5 × 109 cm2 / 7.07 × 10-14 cm2
Number of NH3 molecules = 3.54 × 1023

Step 3: Calculate the volume of NH3 adsorbed on the surface of the charcoal at STP

Given:
- STP (Standard Temperature and Pressure) conditions: 0°C (273 K) and 1 atm (760 mmHg)
- Volume of 1 mole of any gas at STP = 22.4 L = 22.4 × 103 cm3

Since 1 mole of NH3 contains 3.54 × 1023 molecules, the volume of NH3 adsorbed on the surface of the charcoal can be calculated as follows:

Volume of NH3 adsorbed = (Number of NH3 molecules / Avogadro's number) × Volume of 1 mole of NH3 at STP
Volume of NH3 adsorbed = (3.54 × 1023 / 6.022 × 1023) × (22.4 × 103 cm3)
Volume of NH3 adsorbed = 0.588 × (22.4

Answer

Answer

Calculation of the surface area of activated charcoal
---------------------------------------------
To calculate the surface area of activated charcoal, we are given that 1 g of activated charcoal has a surface area of 103 m^2.

Since we are given the surface area in square meters, we need to convert it to square centimeters for ease of calculation.

1 m^2 is equal to 10,000 cm^2, so the surface area of 1 g of activated charcoal is equal to 103 x 10,000 = 1,030,000 cm^2.

Since we need to find the surface area of 25 g of charcoal, we can multiply the surface area of 1 g by 25:

1,030,000 cm^2/g x 25 g = 25,750,000 cm^2.

Calculation of the number of NH3 molecules adsorbed
---------------------------------------------
To calculate the number of NH3 molecules adsorbed, we need to consider the complete monolayer coverage assumption and the diameter of the NH3 molecule.

The diameter of the NH3 molecule is given as 0.3 nm.

To calculate the number of NH3 molecules adsorbed, we need to find the area occupied by each NH3 molecule on the surface of the charcoal.

The area occupied by each NH3 molecule can be calculated using the formula for the area of a circle:

Area = π x (diameter/2)^2

Plugging in the values:

Area = π x (0.3 nm/2)^2 = π x (0.15 nm)^2 = π x 0.0225 nm^2.

Now, we can calculate the number of NH3 molecules adsorbed by dividing the surface area of the charcoal by the area occupied by each NH3 molecule:

Number of NH3 molecules adsorbed = surface area of charcoal / area occupied by each NH3 molecule.

Number of NH3 molecules adsorbed = 25,750,000 cm^2 / (π x 0.0225 nm^2).

Since the dimensions of the surface area and the area occupied by each NH3 molecule are in different units, we need to convert them to the same unit.

1 nm = 1 x 10^-7 cm, so the area occupied by each NH3 molecule is equal to 0.0225 nm^2 x (1 x 10^-7 cm/nm)^2 = 2.25 x 10^-15 cm^2.

Plugging in the values:

Number of NH3 molecules adsorbed = 25,750,000 cm^2 / (π x 2.25 x 10^-15 cm^2).

Number of NH3 molecules adsorbed ≈ 3.627 x 10^22.

Final conversion to cm3 at STP
---------------------------------------------
To convert the number of NH3 molecules adsorbed to cm3 at STP, we need to divide by Avogadro's number (6.022 x 10^23 molecules/mol) and multiply by the molar volume of a gas at STP (22.4 L/mol or 22,400 cm^3/mol).

Number of NH3 molecules adsorbed in cm3 at STP = (3.627 x 10^22 molecules) / (6.022 x 10^23 molecules/mol) x 22,

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