I am stuck at trying to derive the expression for ?S_{mixing}

For a perfect gas mixture, the chemical potential of component i is given as:

?_{i,mixture} = ?_{i,REF} + RT.ln(P_{i}/P_{REF})

from G = H - TS, we arrive at dG = dH - TdS - SdT

since dH = TdS + V.dP, then dG = VdP - SdT

At constant pressure, dP = 0 **=>** dG = -SdT **=>** S = -(dG/dT)_{P}

Hence, s_{i,mixture} = -(d?_{i}/dT)_{P}

s_{i,mixture} = -(d?/dT)_{P} = -d(?_{i,REF})/dT - (d/dT)(RT.ln(P_{i}/P_{REF})) = -d(?_{REF})/dT - (d/dT)(RT.ln(n_{i}RT/P_{REF}V))

s_{i,mixture} = s_{i,REF} - R.ln(n_{i}RT/P_{REF}V) - RT/T = s_{i,REF} - R.ln(n_{i}RT/P_{REF}V) - R

s_{i,mixture} = s_{i,REF} - R( ln(n_{i}RT/P_{REF}V) + 1 ) =s_{i,REF} - R( ln(P_{i}/P_{REF}) + 1 )

Then I got stuck here...