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 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:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: