\(a,n_{Zn}=\dfrac{13}{65}=0,2\left(mol\right)\\ PTHH:Zn+2HCl\rightarrow ZnCl_2+H_2\\ \text{Vì }\dfrac{n_{Zn}}{1}< \dfrac{n_{HCl}}{2}\text{ nên sau p/ứ }HCl\text{ dư}\\ \Rightarrow n_{H_2}=n_{Zn}=0,2\left(mol\right)\\ \Rightarrow V_{H_2\left(đktc\right)}=0,2\cdot22,4=4,48\left(l\right)\\ b,\text{Chất còn dư là }HCl\\ n_{HCl\left(dư\right)}=n_{HCl\text{ đề}}-n_{HCl\text{ phản ứng}}=0,5-0,4=0,1\left(mol\right)\\ \Rightarrow m_{HCl\text{ dư}}=0,1\cdot36,5=3,65\left(g\right)\)