\(n_K=\dfrac{7.8}{39}=0.2\left(mol\right)\)
\(2K+2H_2O\rightarrow2KOH+H_2\)
\(0.2.......................0.2......0.1\)
\(V_{H_2}=0.1\cdot22.4=2.24\left(l\right)\)
\(m_{KOH}=0.2\cdot56=11.2\left(g\right)\)
\(m_{dd_{KOH}}=7.8+400-0.1\cdot2=407.6\left(g\right)\)
\(C\%KOH=\dfrac{11.2}{407.6}\cdot100\%=2.74\%\)