\(a,PTHH:K_2O+H_2O\to 2KOH\\ n_{K_2O}=\dfrac{18,8}{94}=0,2(mol)\\ \Rightarrow n_{KOH}=0,4(mol)\\ \Rightarrow C\%_{KOH}=\dfrac{0,4.56}{18,8+121,2}.100\%=16\%\\ b,n_{KOH}=\dfrac{50.16\%}{56}=\dfrac{1}{7}(mol)\\ PTHH:2KOH+H_2SO_4\to K_2SO_4+2H_2O\\ \Rightarrow n_{H_2SO_4}=\dfrac{2}{7}(mol)\\ \Rightarrow m_{dd_{H_2SO_4}}=\dfrac{\dfrac{2}{7}.98}{20\%}=140(g)\)
\(n_{K_2SO_4}=n_{KOH}=\dfrac{1}{7}(mol)\\ \Rightarrow m_{K_2SO_4}=\dfrac{1}{7}.174=24,86(g)\\ \Rightarrow C\%_{K_2SO_4}=\dfrac{24,86}{50+140}.100\%=13,08\%\)