You are given one litre each of 0.5 M HCl and 0.2 M HCl. Calculate the ratio in which they should be mixed so as to give maximum volume of 0.4 M HCl. What will be this volume ?

You are given one litre each of 0.5 M HCl and 0.2 M HCl. Calculate the

1.	You are given one litre each of 0.5 M HCl and 0.2 M HCl. Calculate the ratio in which they should be mixed so as to give maximum volume of 0.4 M HCl. What will be this volume ?
Answer» Solution :Suppose V LITRE of 0.5 M HCl is MIXED with 1 L of 0.2 M HCl to prepare 0.4 M HCl. Then, `""M_(1)V_(1)+M_(2)V_(2)=M_(3)(V_(1)+V_(2))` gives `""0.5xxV+0.2xx1=0.4(V+1)` `"or"0.5V+0.2=0.4V+0.4"or"0.1 V=0.2 "or"V=2L` Thus, 2 L of 0.5 M HCl is needed which is not available. Again, Suppose V litre of 0.2 M HCl should be added to 1 L of 0.5 M HCl to obtain 0.4 M HCl. Then `M_(1)V_(1)+M_(2)V_(2)=M_(3)(V_(1)+V_(2))` `0.2xxV+0.5xx1=0.4(V+1)` `"or"0.2V+0.5=0.4V+0.4"or"0.2V=0.1"or"V=0.5L` Thus, 0.5 L of 0.2 M HCl should be added to 1 L of 0.5 M HCl to obtain 0.4 M HCl. Volume of 0.4 M HCl obtained = 1.5 L. Thus, 0.5 L of 0.2 M HCl and 0.2 M HCl should be mixed = 1 L : 0.5 L = 2 : 1 Alternatively, suppose x L of 0.5 M HCl are mixed with y L of 0.2 M HCl to make 0.4 M HCl. Then `M_(1)V_(1)+M_(2)V_(2)=M_(3)(V_(1)+V_(2))` `0.5x+0.2y=0.4(x+y)` `"or"0.1x=0.2y"or"(x)/(y)=(2)/(1)` Thus, 0.5 M HCl and 0.2 M HCl should be mixed in the RATIO of `2:1`. As maximum amount availableis 1 L of each, this MEANS 1 L of 0.5 M HCl should be mixed with 0.5 L of 0.2 M HCl, i.e., in the ratio`2:1` Volume of 0.4 M HCl obtained = 1.5 L.