Linebreak in multirow using tabularx

Here is a solution. I have used multirowcell from the makecell package for the multiline multirows and left the units outside of textbf because units won't be done bold. The second column is fit to the "Molar mass" width.

EDIT: In fact multirow{2}={textbf{Molar mass} {}[$si{grampermol}$] } works as well as multirowcell, and for the other one similar.

documentclass[a4paper, 11pt]{article}
usepackage[margin=2cm]{geometry}

% language
usepackage[utf8]{inputenc} 

% graphics
usepackage{array,multirow,graphicx} 

% units 
usepackage{siunitx}

% chemistry 
usepackage{ghsystem}
usepackage[version=4]{mhchem} 

% tables
usepackage{ragged2e} 
usepackage{booktabs, tabularx}
%____________________________________________________________________________________________________________
newcolumntype{B}[1]{>{scriptsizeRaggedRighthspace{0pt}}p{#1}}
newcolumntype{L}{>{scriptsizeRaggedRighthspace{0pt}}X}
newlengthcolwidth
newlengthcolwidthb
%____________________________________________________________________________________________________________
% figures 
usepackage{float}
%____________________________________________________________________________________________________________
usepackage{makecell}

begin{document}

begin{table}[ht!]
settowidthcolwidth{textbf{Solution}} % <-- need to use textbf to get correct measurement
settowidthcolwidthb{textbf{Molar mass}} % <-- need to use textbf to get correct measurement
begin{tabularx}{textwidth}{@{} B{colwidth} @{} B{colwidthb}@{} *{7}{L} @{}} 
toprule 
 multirow{2}*{textbf{Solution}}   &
 multirowcell{2}[0pt][l]{textbf{Molar mass} {}[$si{grampermol}$] }  &
 multirowcell{2}[0pt][l]{textbf{V mass} {}[si{milliliter}] }  &
    multicolumn{3}{c}{textbf{Amount of substance [$si{millimol}$]}  }     &   
    multicolumn{3}{c}{textbf{Mass [$si{gram}$]}  }    
       
cmidrule(lr){4-6} cmidrule(lr){7-9}
 & & & ce{KH2PO4} & ce{Na2HPO4} & ce{NaCl} & ce{KH2PO4} & ce{Na2HPO4} & ce{NaCl} 
midrule
$ce{KH2PO4}$ stock     &  num{150}  & $num{1.5}$  & -                 & $num{}$ &  $num{}$ & -         & $num{}$ 
$ce{Na2HPO4}$ stock    &  num{100}  & -             & $num{1}$      & $num{}$ & -            &num{}     & $num{}$ 
bottomrule
end{tabularx}
%endtabularx
end{table}

end{document}

With {NiceTabular} of nicematrix.

documentclass[a4paper, 11pt]{article}
usepackage[margin=2cm]{geometry}
usepackage{siunitx}
usepackage[version=4]{mhchem} 
usepackage{booktabs}
usepackage{nicematrix}

begin{document}

begin{table}[ht!]
small
begin{NiceTabular}{@{}l S[table-format=3] S[table-format=1.1] *{6}{c} @{}} 
toprule 
Block{2-1}{bfseries Solution} 
& Block{2-1}<bfseries>{Molar mass{} [si{grampermol}]} 
& Block{2-1}<bfseries>{V stock{} [si{milliliter}]} 
& Block{1-3}<bfseries>{Amount of substance [si{millimol}]} &&
& Block{1-3}{bfseries Mass [si{gram}]} 
cmidrule(r){4-6} cmidrule(l){7-9}
                     &       &      & ce{KH2PO4} & ce{Na2HPO4} & ce{NaCl} & ce{KH2PO4} & ce{Na2HPO4} & ce{NaCl}
midrule
ce{KH2PO4} stock    &  150  & 1.5  & -           &              &           & -           &              &     
ce{Na2HPO4} stock   &  10   & {-}  & 1           &              & -         &             &              &     
bottomrule         
end{NiceTabular}
end{table}

end{document}