
The molecular weight of \( C_8H_8O_2 \) is calculated as:
Molecular weight = \( 12 \times 8 + 1 \times 8 + 16 \times 2 = 96 + 8 + 32 = 136 \)
Next, we calculate the moles of product \( D \) formed:
Moles of product \( D \) = \( \frac{15}{3} \times 0.8 \times 0.5 = \frac{3}{3} = 1 \)
Therefore, the weight of product \( D \) is:
Weight of product \( D \) = \( 1 \times 136 = 136 \, \text{g} \)
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).

Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?
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