If the standard enthalpy change $\left(\Delta_{r} H^{\theta}\right)$ for a certain reaction at $298 \ K$ and constant pressure is $-1860 \ kJ \ mol^{-1}$,and the standard entropy change $\left(\Delta_{\text{sys}} S^{\theta}\right)$ of the same reaction is $-550 \ J \ K^{-1} \ mol^{-1}$,which one of the following statements is correct?

  • A
    $\left(\Delta_{\text{sys}} S^{\theta}\right) + \Delta_{\text{surr}} S^{\theta} = -7692 \ J \ mol^{-1} \ K^{-1}$,the reaction is spontaneous
  • B
    $\left(\Delta_{\text{sys}} S^{\theta}\right) + \Delta_{\text{surr}} S^{\theta} = -5692 \ J \ mol^{-1} \ K^{-1}$,the reaction is non-spontaneous
  • C
    $\left(\Delta_{\text{sys}} S^{\theta}\right) + \Delta_{\text{surr}} S^{\theta} = +5692 \ J \ mol^{-1} \ K^{-1}$,the reaction is spontaneous
  • D
    $\left(\Delta_{\text{sys}} S^{\theta}\right) + \Delta_{\text{surr}} S^{\theta} = +7692 \ J \ mol^{-1} \ K^{-1}$,the reaction is non-spontaneous

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The free energy change for the following reactions are given below:
$C_2H_{2(g)} + \frac{5}{2}O_{2(g)} \to 2CO_{2(g)} + H_2O_{(l)}; \Delta G^o = -1234 \ kJ$
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