0.05M CuSO$_4$ when treated with 0.01M K$_2$Cr$_2$O$_7$ gives green colour solution of Cu$_2$Cr$_2$O$_7$. The \[ \text{[SPM : Semi Permeable Membrane]} \]\(K_2Cr_2O_7\) \(CuSO_4\) Side X SPM Side Y
Due to osmosis:
| \(K_2Cr_2O_7\) | \(CuSO_4\) | |
| Side X | SPM | Side Y |
Due to osmosis:
- Green colour formation observed on side Y.
- Green colour formation observed on side X.
- Molarity of\(K_2Cr_2O_7\)solution is lowered.
- Molarity of\(CuSO_4\)solution is lowered.
The Correct Option is D
Approach Solution - 1
To solve this problem, we need to understand the concept of osmosis and how it affects the molarity of solutions separated by a semipermeable membrane (SPM).
In the given scenario, we have the following setup:
| \(K_2Cr_2O_7\) | \(CuSO_4\) | |
| Side X | SPM | Side Y |
In this arrangement, \(K_2Cr_2O_7\) is on Side X and \(CuSO_4\) is on Side Y. Osmosis refers to the movement of solvent molecules through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration.
Now, let's analyze the options:
- Green colour formation observed on side Y.
- Green colour formation observed on side X.
- Molarity of \(K_2Cr_2O_7\) solution is lowered.
- Molarity of \(CuSO_4\) solution is lowered.
Since the solutions are separated by a semipermeable membrane, only the solvent (typically water) can move to equalize solute concentrations, not the solute itself. Therefore, any change in molarity due to osmosis would typically be a result of water moving from the side with lower solute concentration to the side with higher solute concentration, making the latter solution more dilute.
In this situation, osmosis will cause the water to move from the \(K_2Cr_2O_7\) side (Side X) to the \(CuSO_4\) side (Side Y) because the \(CuSO_4\) solution is involved in forming the green complex \(Cu_2Cr_2O_7\), thereby reducing its effective concentration.
Thus, the molarity of the \(CuSO_4\) solution is lowered as water moves into Side Y to equalize concentration due to osmosis.
Therefore, the correct option is:
Molarity of \(CuSO_4\) solution is lowered.
Approach Solution -2
Due to osmosis, the solvent molecules from side Y (CuSO4) diffuse across the semi-permeable membrane (SPM) into side X (K2Cr2O7). This dilution effect causes the molarity of the CuSO4 solution (side Y) to decrease over time.
- CuSO4 reacts with K2Cr2O7, forming Cu2Cr2O7, which is responsible for the green color.
- The green color is observed due to the formation of Cu2Cr2O7, but the key change is in the molarity of the CuSO4 solution on side Y, which decreases as the solvent diffuses.
Thus the correct answer is Option 4.
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