Given below are two statements:
Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent.
Statement II: Sodium metal can be used to dry diethyl ether and not ethyl alcohol.
In the light of the given statements, choose the correct answer from the options given below:
Statement-I is correct because both the given ethers (Di-ethyl ether and butan-1-ol) are soluble in water. This solubility is due to the ability of the molecules to form hydrogen bonds with water molecules. Di-ethyl ether and butan-1-ol are miscible to almost the same extent, with 7.5 gm and 9 gm dissolving per 100 ml of water, respectively. This occurs due to hydrogen bonding between the oxygen atom of the ether and the hydrogen atom of water molecules. Hence, the statement is correct due to the influence of hydrogen bonding in the solubility of these compounds in water.
Statement-II is also correct because sodium metal is not used with ethyl alcohol. In this case, hydrogen gas (H2) is released when sodium reacts with ethyl alcohol, as sodium displaces the hydrogen atom from the alcohol. However, this reaction does not involve sodium directly with ethyl alcohol, as the reaction leads to the release of hydrogen gas. Therefore, the statement is correct because sodium does not react directly in the same manner as with other alcohols, and hydrogen gas is released instead.
Let \( C_{t-1} = 28, C_t = 56 \) and \( C_{t+1} = 70 \). Let \( A(4 \cos t, 4 \sin t), B(2 \sin t, -2 \cos t) \text{ and } C(3r - n_1, r^2 - n - 1) \) be the vertices of a triangle ABC, where \( t \) is a parameter. If \( (3x - 1)^2 + (3y)^2 = \alpha \) is the locus of the centroid of triangle ABC, then \( \alpha \) equals: