def Rachford_Rice_flash_error(V_over_F, zs, Ks):
return sum([zi*(Ki-<NUM_LIT:1.>)/(<NUM_LIT:1.>+V_over_F*(Ki-<NUM_LIT:1.>)) for Ki, zi in zip(Ks, zs)])<EOL>
r'''Calculates the objective function of the Rachford-Rice flash equation.
    This function should be called by a solver seeking a solution to a flash
    calculation. The unknown variable is `V_over_F`, for which a solution
    must be between 0 and 1.

    .. math::
        \sum_i \frac{z_i(K_i-1)}{1 + \frac{V}{F}(K_i-1)} = 0

    Parameters
    ----------
    V_over_F : float
        Vapor fraction guess [-]
    zs : list[float]
        Overall mole fractions of all species, [-]
    Ks : list[float]
        Equilibrium K-values, [-]

    Returns
    -------
    error : float
        Deviation between the objective function at the correct V_over_F
        and the attempted V_over_F, [-]

    Notes
    -----
    The derivation is as follows:

    .. math::
        F z_i = L x_i + V y_i

        x_i = \frac{z_i}{1 + \frac{V}{F}(K_i-1)}

        \sum_i y_i = \sum_i K_i x_i = 1

        \sum_i(y_i - x_i)=0

        \sum_i \frac{z_i(K_i-1)}{1 + \frac{V}{F}(K_i-1)} = 0

    Examples
    --------
    >>> Rachford_Rice_flash_error(0.5, zs=[0.5, 0.3, 0.2],
    ... Ks=[1.685, 0.742, 0.532])
    0.04406445591174976

    References
    ----------
    .. [1] Rachford, H. H. Jr, and J. D. Rice. "Procedure for Use of Electronic
       Digital Computers in Calculating Flash Vaporization Hydrocarbon
       Equilibrium." Journal of Petroleum Technology 4, no. 10 (October 1,
       1952): 19-3. doi:10.2118/952327-G.