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.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: