In a one-litre flask, \( 6 \) moles of \( \mathrm{A} \) undergoes the reaction \( \mathrm{A(g)} \rightleftharpoons \mathrm{P(g)} \). The progress of product formation at two temperatures (in Kelvin), \( T_1 \) and \( T_2 \), is shown in the figure: 
If \( T_1 = 2T_2 \) and \( \left( \Delta G_2^\ominus- \Delta G_1^\ominus \right) = RT_2 \ln x \), then the value of \( x \) is _______.
\([ \Delta G_1^\ominus - \Delta G_2^\ominus ]\) are standard Gibb’s free energy change for the reaction at temperatures \( T_1 \) and \( T_2 \), respectively]
