8) We have two solutions of calcium nitrate $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}$ in $0.580 \mathrm{M}$ and $1.4 \mathrm{M}$ concentrations. A new solution is prepared by mixing $(Y+120) \mathrm{ml}$ from the $1.4 \mathrm{M}$ solution and $220 \mathrm{ml}$ from 0.589 $\mathrm{M}$ solution. Calculate the concentration of the new solution.

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∻Solution∻ ‖ 1 ⋮ **Identify the volumes and concentrations**: We have two solutions of calcium nitrate, $Ca(NO_3)_2$. The first solution has a concentration of $0.580 \, M$ and a volume of $220 \, ml$. The second solution has a concentration of $1.4 \, M$ and a volume of $(Y + 120) \, ml$. ‖ ‖ 2 ⋮ **Calculate the moles of solute in each solution**: - For the $0.580 \, M$ solution: $$ \text{Moles of } Ca(NO_3)_2 = 0.580 \, M \times 0.220 \, L = 0.1276 \, \text{moles} $$ - For the $1.4 \, M$ solution: $$ \text{Moles of } Ca(NO_3)_2 = 1.4 \, M \times \left(\frac{Y + 120}{1000}\right) \, L = 1.4 \times \left(\frac{Y + 120}{1000}\right) \, \text{moles} $$ ‖ ‖ 3 ⋮ **Sum the moles of solute**: $$ \text{Total moles of } Ca(NO_3)_2 = 0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right) $$ ‖ ‖ 4 ⋮ **Sum the volumes of the solutions**: $$ \text{Total volume} = 220 \, ml + (Y + 120) \, ml = (Y + 340) \, ml = \frac{Y + 340}{1000} \, L $$ ‖ ‖ 5 ⋮ **Calculate the concentration of the new solution**: $$ \text{Concentration} = \frac{\text{Total moles of } Ca(NO_3)_2}{\text{Total volume}} = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ $$ = \frac{0.1276 + 1.4 \times \left(\frac{Y + 120}{1000}\right)}{\frac{Y + 340}{1000}} $$ \[ ◊What is the formula for calculating the concentration of a solution when mixing two solutions of different concentrations?⍭ Generate me a similar question◊]‖

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