Into a barrel containing 0769 m3 of water containing 00555 M

Into a barrel containing 0.769 m^3 of water containing 0.0555 M of a blue dye you pour V_2 yd^3 of water containing 3.43 mol/L of the dye. The final concentration of the dye in the barrel is 57.8 mol/m^3 after it\'s well-mixed.

Solution

Assuming the question is find V₂ as it is the only variable in the question

Barrel contains .769m³ = 769 L (let it be denoted by V₁) water containing the dye of molarity 0.0555M

V₂ yd³ of water with molarity of dye =3.43M is added to the barrel. Note:molarity is mole per litre i.e. M and mol/L are the same

1 yd (yard) = 36 inches = 36*2.54*10^-2m = 0.9144m

1 yd³ = .7646 m³ = 764.6 L

Volume added to the barrel = 764.6V₂ L

Final concentration = 57.8 mol/m³ = 0.0578 M , as1000L = 1m³

We know that no of moles of dye doesn\'t change so, moles of dye in two solution = moles of dye in mixture

0.0555*769 + 3.43*764.6*V₂ = (769 + 764.6*V₂)*0.0578

2.578*V₂ = 1.7687 x 10^-3

V₂ = 6.861 x 10^-4 yd³