VE13. Erikaal

Ülesanne. Vee tihedus on 1 g/cm3. Etanooli tihedus on 0,79 g/cm3. Tehakse etanooli ja vee lahus, mille tihedus on 0,916 g/cm3. Kui suur on etanooli kontsentratsioon lahuses?

 

Lahendus.

Paneme kirja andmed:
rho subscript v e s i end subscript equals 1 fraction numerator g over denominator c m cubed end fraction rho subscript e tan o o l end subscript equals 0 comma 79 fraction numerator g over denominator c m cubed end fraction rho subscript s e g u end subscript equals 0 comma 916 fraction numerator g over denominator c m cubed end fraction minus negative negative negative negative negative negative negative negative negative negative x minus ?

Koostame võrrandisüsteemi, kus x on etanooli kontsentratsioon ning y vee kontsentratsioon:
open curly brackets table attributes columnalign left end attributes row cell rho subscript v e s i end subscript times y plus rho subscript e tan o o l end subscript times x equals rho subscript s e g u end subscript end cell row cell y plus x equals 1 end cell end table close y equals 1 minus x rho subscript v e s i end subscript times left parenthesis 1 minus x right parenthesis plus rho subscript e tan o o l end subscript times x equals rho subscript s e g u end subscript rho subscript v e s i end subscript minus rho subscript v e s i end subscript x plus rho subscript e tan o o l end subscript times x equals rho subscript s e g u end subscript x left parenthesis rho subscript e tan o o l end subscript minus rho subscript v e s i end subscript right parenthesis equals rho subscript s e g u end subscript minus rho subscript v e s i end subscript x equals fraction numerator rho subscript s e g u end subscript minus rho subscript v e s i end subscript over denominator rho subscript e tan o o l end subscript minus rho subscript v e s i end subscript end fraction equals fraction numerator left parenthesis 0 comma 916 minus 1 right parenthesis begin display style fraction numerator g over denominator c m cubed end fraction end style over denominator left parenthesis 0 comma 79 minus 1 right parenthesis fraction numerator g over denominator c m cubed end fraction end fraction equals 0 comma 4

VASTUS: Etanooli kontsentratsioon lahuses on 0,4 ehk 40%. Vett on järelikult 60%.