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The solution of H_(2)SO_(4) of molarities x and y are mixed in the ratio of V_(1) mL : V_(2) mL of form a solution of molarity M_(1). If theyare mixed in the ratio of V_(2)mL : V_(1)mL , they form a solution of molarity M_(2). Given (V_(1))/(V_(2))gt 1 and (M_(1))/(M_(2))=(5)/(4), calculate the ratio x:y. |
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Answer» Solution :`{:(,M_(1)'V_(1)'+M_(2)'V_(2)'=M_(3)'(V_(1)'V_(2)')),("In 1st case,",x xxV_(1)+y xx V_(2)=M_(1)(V_(1)+V_(2))"...(i)"),("In 2nd case, ", x xx V_(2)+y xxV_(1)=M_(2)(V_(1)+V_(2))"...(ii)"):}` DIVIDING eqn. (i) eqn. (ii), weget `(xV_(1)+yV_(2))/(xV_(2)+yV_(1))=(M_(1))/(M_(2))=(5)/(4)"GIVEN)"` `"or"4(xV_(1)+yV_(2))=5(xV_(2)+yV_(1))` `"or"4xV_(1)+4yV_(2)=5xV_(2)+5yV_(1)` `"or"(4x-5y)V_(1)=(5x-4y)V_(2)` `"or"(V_(1))/(V_(2))=(5x-4y)/(4x-5y)=(x)/(y)"(Given)"` `"or"((5x)/(y)-4)/((4x)/(y)-5)=(x)/(y)"(Dividing numerator and denominator by y)"` `"or"(5x)/(y)-4=(4x^(2))/(y^(2))-4(x)/(y)"or"(4x^(2))/(y^(2))-10(x)/(y)+4=0` `"Putting"(x)/(y)=z,4z^(2)-10z+4=0` `therefore""z=(-b pmsqrt(b^(2)-4ac))/(2a)=(10pmsqrt(100-64))/(8)=(10pm6)/(8)=(16)/(8)"or"(4)/(8)," i.e., 2 or "(1)/(2)` `"As"(x)/(y) gt 1," HENCE "(x)/(y)=2," i.e., " x:y = 2:1` |
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