The water-gas reaction needs very high temperatures. The water-gas shift reac tion, aided by a catalyst, can operate effectively at lower temperatures.
The water-gas reaction requires high temperatures for the reaction to proceed effectively:
Reaction Temperature: \( T_1 \approx 1270 \, \text{K} \)
The water-gas shift reaction is typically carried out at lower temperatures in the presence of a catalyst:
Reaction Temperature: \( T_2 \approx 673 \, \text{K} \)
The temperature for the water-gas reaction (\( T_1 \)) is significantly higher than the temperature for the water-gas shift reaction (\( T_2 \)). Therefore:
\( T_1 > T_2 \)
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