The values of X, Y, and Z in the following chemical equation are respectively:
\( S_8 + X HNO_3 ({conc.}) \rightarrow Y H_2SO_4 + X NO_2 + Z H_2O \)
36, 6, 18
48, 8, 24
48, 8, 16
24, 8, 12
Step 1: Balance the reaction for sulfur \(S_8\), ensuring that the atoms on both sides are equal for all elements.
Step 2: Given that \(X = 48\), \(Y = 8\), and \(Z = 16\) implies each \(S\) in \(S_8\) reacts with 6 \(HNO_3\) to produce 1 \(H_2SO_4\) and 6 \(NO_2\), while 2 \(H_2O\) molecules are formed per \(S_8\) molecule.
Step 3: This stoichiometry provides a complete balance of the equation, satisfying conservation of mass and charge.
Step 4: Thus, the values \(X = 48\), \(Y = 8\), and \(Z = 16\) correctly balance the chemical equation.
Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then: