Chemical Engineering
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A binary liquid mixture consists of two species $1$ and $2$. Let $\gamma$ and $x$ represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, $\ln \gamma_1 \textit{ vs. } x_1$ and $\ln \gamma _2 \textit{ vs. } x_1$ are plotted. A tangent drawn to the $\ln \gamma_1 \textit{ vs. } x_1$ curve at a mole fraction of $x_1=0.2$ has a slope $=-1.728$.

The slope of the tangent drawn to the $\ln \gamma_2 \textit{ vs. } x_1$ curve at the same mole fraction is ___________ ( correct to $3$ decimal places)
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