\[ \Delta G^\circ = -RT \ln K_p \]
\[ \Delta G^\circ = -8.314 \times 10^{-3} \times 298 \times \ln(2.47 \times 10^{-29}) \]
\[ = -8.314 \times 10^{-3} \times 298 \times (-65.87) \]
\[ = 163.19 \, \text{kJ} \]
The standard heat of formation, in kcal/mol, of $Ba^{2+}$ is:
Given: Standard heat of formation of SO₄²⁻(aq) = -216 kcal/mol, standard heat of crystallization of BaSO₄(s) = -4.5 kcal/mol, standard heat of formation of BaSO₄(s) = -349 kcal/mol.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: