A solution showing negative deviation from Raoult’s law has lower vapour pressure than expected because the interactions between the components are stronger than in the pure liquids. This results in a decreased vapour pressure, which leads to an increase in boiling point.
For solutions showing negative deviation:
$$ P_T < P_A^0 X_A + P_B^0 X_B $$
where \( P_T \) is the total vapour pressure, \( P_A^0 \) and \( P_B^0 \) are the vapour pressures of pure components, and \( X_A \) and \( X_B \) are their mole fractions.
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32