1 gm charcoal having surface area 3.01x10² m is mixed in 100ml of 0.5M...
1 gm charcoal having surface area 3.01x10² m is mixed in 100ml of 0.5M...
Surface Area of Charcoal
To find the surface area occupied by one molecule of acetic acid, we need to consider the reaction between charcoal and acetic acid. The first step is to determine the surface area of the given mass of charcoal.
Given:
Mass of charcoal = 1 gm
Surface area of charcoal = 3.01 × 10² m
Calculating Moles of Acetic Acid
Next, we need to calculate the moles of acetic acid present in the solution. We are given that the initial concentration of acetic acid is 0.5M and the volume is 100ml.
The formula to calculate moles of a substance is:
Moles = Concentration × Volume
Moles of acetic acid = 0.5M × 0.1L (since 100ml = 0.1L)
Moles of acetic acid = 0.05 moles
Reaction between Charcoal and Acetic Acid
The reaction between charcoal and acetic acid can be represented as:
C + 2CH₃COOH -> CH₃COOC + CH₃COOH
From the balanced equation, we can see that 1 mole of charcoal reacts with 2 moles of acetic acid.
Therefore, moles of charcoal = 0.05 / 2 = 0.025 moles
Calculating the Surface Area Occupied by One Molecule of Acetic Acid
Now, we can calculate the surface area occupied by one molecule of acetic acid.
Surface area occupied by 1 mole of acetic acid = 3.01 × 10² m
Surface area occupied by 0.025 moles of acetic acid = (3.01 × 10² m) / 0.025
Surface area occupied by one molecule of acetic acid = (3.01 × 10² m) / (0.025 × Avogadro's number)
Avogadro's number (Nₐ) = 6.022 × 10²³
Surface area occupied by one molecule of acetic acid = (3.01 × 10² m) / (0.025 × 6.022 × 10²³)
Final Answer
The surface area occupied by one molecule of acetic acid is equal to the calculated value above.
Explanation
In this problem, we first calculated the moles of acetic acid present in the solution using its concentration and volume. Then, we determined the moles of charcoal based on the reaction between charcoal and acetic acid. Finally, we used the given surface area of charcoal to find the surface area occupied by one molecule of acetic acid. This calculation involved converting moles to molecules using Avogadro's number.
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