Question

Into a barrel containing 33.2 bbl (US) of water containing 0.0012 mol/L of a blue dye you pour V2 yd3 of water containing 8.91 M of the dye. The final concentration of the dye in the barrel is 7.91 mol/m3 after it's well-mixed. What is V2 is yd^3?

Answer 1

Answer on Question #54643-Engineering-Chemical Engineering

Into a barrel containing 33.2 bbl (US) of water containing 0.0012 mol/L of a blue dye you pour V2 yd3 of water containing 8.91 M of the dye. The final concentration of the dye in the barrel is 7.91 mol/m3 after it's well-mixed. What is V2 is yd^3?

Solution

The final concentration of the dye in the barrel is

$$\frac {v}{V} = \frac {v _ {1} + v _ {2}}{V _ {1} + V _ {2}} \rightarrow \frac {v}{V} V _ {1} + \frac {v}{V} V _ {2} = \frac {v _ {1}}{V _ {1}} V _ {1} + \frac {v _ {2}}{V _ {2}} V _ {2}.$$ $$V _ {2} = \frac {\frac {v}{V} - \frac {v _ {1}}{V _ {1}}}{\frac {v _ {2}}{V _ {2}} - \frac {v}{V}} V _ {1} = \frac {7.91 \cdot 0.001 \frac {\mathrm {mol}}{\mathrm {L}} - 0.0012 \frac {\mathrm {mol}}{\mathrm {L}}}{8.91 \frac {\mathrm {mol}}{\mathrm {L}} - 7.91 \cdot 0.001 \frac {\mathrm {mol}}{\mathrm {L}}} 33.2 \cdot 0.155961 \mathrm {yd} ^ {3} = 0.0039 \mathrm {yd} ^ {3}.$$

Answer: 0.0039 yd³.