$a\big)$
$Na+H_2O\to NaOH+\frac{1}{2}H_2$
$Ba+2H_2O\to Ba(OH)_2+H_2$
$NaOH+HNO_3\to NaNO_3+H_2O$
$Ba(OH)_2+2HNO_3\to Ba(NO_3)_2+2H_2O$
$b\big)$
Đặt $n_{Na}=x(mol);n_{Ba}=y(mol)$
Theo PT: $\frac{1}{2}x+y=n_{H_2}=\frac{4,48}{22,4}=0,2(1)$
Vì trung hòa $\frac{1}{2}B$
$\to n_{NaOH(dùng)}=\frac{1}{2}x;n_{Ba(OH)_2(dùng)}=\frac{1}{2}y$
Theo PT: $n_{NaNO_3}=\frac{1}{2}x;n_{Ba(NO_3)_2}=\frac{1}{2}y$
$\to \frac{1}{2}x.85+\frac{1}{2}y.261=21,55(2)$
Từ $(1)(2)\to x=0,2(mol);y=0,1(mol)$
$\to m_{Na}=0,2.23=4,6(g);m_{Ba}=0,1.137=13,7(g)$
Theo PT: $\sum n_{HNO_3}=\frac{1}{2}x+y=0,2(mol)$
$\to V_{dd\,HNO_3}=\frac{0,2}{2}=0,1(l)=100(ml)$