0.1 mole of compound S will weigh ....... g,
(given the molar mass in g mol\(^{-1}\) \( {C} = 12, \, {H} = 1, \, {O} = 16 )\):
- The compound \( S \) is formed by reducing a secondary alcohol (ethanol) to a hydrocarbon (alkane).
- First, ethanol (\( {CH}_3{CH}_2{OH} \)) reacts with chromium trioxide (\( {CrO}_3 \)) to form acetaldehyde (\( {CH}_3{CHO} \)).
- Then, acetaldehyde undergoes reduction by sodium borohydride (\( {NaBH}_4 \)) to form ethanol (\( {CH}_3{CH}_2{OH} \)) again.
- Further, the reaction with Grignard reagent (\( {CH}_3{MgI} \)) and water (\( {H}_2{O} \)) forms a secondary alcohol.
- Since \( S \) is an alcohol, it will have the same molecular weight as ethanol. The molar mass of ethanol (\( {CH}_3{CH}_2{OH} \)) is calculated as: \[ 12 \times 2 + 1 \times 6 + 16 = 46 \, {g/mol} \] For \( 0.1 \) mole of \( S \), the weight is: \[ {Weight of } S = 0.1 \times 46 = 4.6 \, {g} \] Thus, \( 0.1 \) mole of compound S weighs \( 4.6 \) grams.
If $10 \sin^4 \theta + 15 \cos^4 \theta = 6$, then the value of $\frac{27 \csc^6 \theta + 8 \sec^6 \theta}{16 \sec^8 \theta}$ is:
If the area of the region $\{ (x, y) : |x - 5| \leq y \leq 4\sqrt{x} \}$ is $A$, then $3A$ is equal to
Let $A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \end{bmatrix}$. If for some $\theta \in (0, \pi)$, $A^2 = A^T$, then the sum of the diagonal elements of the matrix $(A + I)^3 + (A - I)^3 - 6A$ is equal to
Let $A = \{ z \in \mathbb{C} : |z - 2 - i| = 3 \}$, $B = \{ z \in \mathbb{C} : \text{Re}(z - iz) = 2 \}$, and $S = A \cap B$. Then $\sum_{z \in S} |z|^2$ is equal to
Let $C$ be the circle $x^2 + (y - 1)^2 = 2$, $E_1$ and $E_2$ be two ellipses whose centres lie at the origin and major axes lie on the $x$-axis and $y$-axis respectively. Let the straight line $x + y = 3$ touch the curves $C$, $E_1$, and $E_2$ at $P(x_1, y_1)$, $Q(x_2, y_2)$, and $R(x_3, y_3)$ respectively. Given that $P$ is the mid-point of the line segment $QR$ and $PQ = \frac{2\sqrt{2}}{3}$, the value of $9(x_1 y_1 + x_2 y_2 + x_3 y_3)$ is equal to