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Comprehension Type
This section contains a passage describing theory, experiments, data, etc. Two questions related to the paragraph have been given. Each question has only one correct answer out of the given 4 options (a), (b), (c) and (d)
 
Passage
Consider the following arrangement in which a solution containing 20 g of haemoglobin in 1 L of the solution is placed in the right compartment and pure water is placed in the left compartment. At equilibrium, the height of the water in the right column is 77.8 mm in excess of the height of the solution in the left column at 298 K.
Q.
Osmotic pressure of the solution is
  • a)
    763 Nm-2
  • b)
    7.63 Nm-2
  • c)
    0.763 Nm-2
  • d)
    76.3 Nm-2
Correct answer is option 'A'. Can you explain this answer?
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Explanation:

The osmotic pressure of a solution can be calculated using the formula:

Osmotic pressure (π) = (n/V)RT

Where:
n = number of moles of solute
V = volume of solution in liters
R = ideal gas constant (8.314 J/(mol·K))
T = temperature in Kelvin

In this case, the solute is haemoglobin and the volume of the solution is 1 L.

Step 1: Calculate the number of moles of haemoglobin:

Given that the solution contains 20 g of haemoglobin, we can calculate the number of moles using the formula:

Number of moles (n) = mass/molar mass

The molar mass of haemoglobin is approximately 64,500 g/mol.

n = 20 g / 64,500 g/mol ≈ 3.1 x 10^-4 mol

Step 2: Calculate the osmotic pressure:

Using the given information that the height of the water in the right column is 77.8 mm in excess of the height of the solution in the left column, we can calculate the difference in heights:

Height difference (h) = 77.8 mm = 0.0778 m

Now we can calculate the osmotic pressure using the formula:

Osmotic pressure (π) = (n/V)RT

Since the volume of the solution is 1 L, we can write:

π = (3.1 x 10^-4 mol / 1 L) * (8.314 J/(mol·K)) * (298 K) = 763 N/m^2

Conclusion:

Therefore, the osmotic pressure of the solution is 763 N/m^2, which is equivalent to 763 Nm^-2. Hence, the correct answer is option 'A'.
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