Balanced chemical equation is:
Ba(OH)2 + 2 HCl ---> BaCl2 + 2 H2O
Here:
M(Ba(OH)2)=0.1 M
M(HCl)=0.15 M
V(Ba(OH)2)=20.0 mL
According to balanced reaction:
2*number of mol of Ba(OH)2 =1*number of mol of HCl
2*M(Ba(OH)2)*V(Ba(OH)2) =1*M(HCl)*V(HCl)
2*0.1 M *20.0 mL = 1*0.15M *V(HCl)
V(HCl) = 26.6667 mL
Answer: 26.7 mL
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