$8MX+5H_2SO_4\rightarrow 4M_2SO_4+H_2S\uparrow+4X_2+4H_2O$$H_2S+Pb(NO_3)_2\rightarrow 2HNO_3+PbS\downarrow$
$X_2\overset{t^o}{\rightarrow}X_2\uparrow$
$\Rightarrow n_{H_2S}=n_{PbS}=0,1 mol\Rightarrow n_{X_2}=0,4 mol\Rightarrow M_{X_2}=\frac{171,2-69,6}{0,4}=254$
$\Rightarrow X_2:I_2$
$n_{BaSO_4}=\frac{1,674.69,6}{232}=0,5022 mol$
$\Rightarrow n_{H_2SO_4}=n_{BaSO_4}+n_{H_2S}=0,6022 mol\Rightarrow C_M=3,011 M$
$M_{M_2SO_4}=\frac{69,6}{0,4}=174\Rightarrow M:K$
$\Rightarrow m=0,8.166=132,8 gam$