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. $\mathrm{A}$ new solution is prepared by mixing $(\mathrm{Y}+120) \mathrm{ml}$ from the $1.4 \mathrm{M}$ solution and $220 \mathrm{ml}$ from 0.589 $M$ solution. Calculate the concentration of the new solution.

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∻Solution∻ ‖ 1 ⋮ **Calculate moles of $\mathrm{Ca(NO_3)_2}$ in the $1.4 \mathrm{M}$ solution**: To find the moles of $\mathrm{Ca(NO_3)_2}$ in the $1.4 \mathrm{M}$ solution, use the molarity equation $n = M imes V$, where $n$ is the number of moles, $M$ is the molarity, and $V$ is the volume in liters. For the $1.4 \mathrm{M}$ solution, the volume is $(Y+120) \mathrm{ml}$, which needs to be converted to liters by dividing by 1000. Thus, $n_{1.4} = 1.4 imes \frac{(Y+120)}{1000}$. ‖ ‖ 2 ⋮ **Calculate moles of $\mathrm{Ca(NO_3)_2}$ in the $0.580 \mathrm{M}$ solution**: Similarly, calculate the moles of $\mathrm{Ca(NO_3)_2}$ in the $0.580 \mathrm{M}$ solution using the molarity equation. The volume is $220 \mathrm{ml}$ or $0.220 \mathrm{L}$. Thus, $n_{0.580} = 0.580 imes 0.220$. ‖ ‖ 3 ⋮ **Calculate total moles of $\mathrm{Ca(NO_3)_2}$ in the mixed solution**: Add the moles from both solutions to find the total moles in the mixed solution: $n_{total} = n_{1.4} + n_{0.580}$. ‖ ‖ 4 ⋮ **Calculate total volume of the mixed solution**: Add the volumes of the two solutions to find the total volume in liters: $V_{total} = \frac{(Y+120)}{1000} + 0.220$. ‖ ‖ 5 ⋮ **Calculate the molarity of the mixed solution**: Use the molarity equation $M = \frac{n}{V}$, where $n$ is the total moles of solute and $V$ is the total volume of the solution in liters. Thus, $M_{mixed} = \frac{n_{total}}{V_{total}}$. ‖ ∻Answer∻ ⚹ $M_{mixed} = \frac{1.4 imes \frac{(Y+120)}{1000} + 0.580 imes 0.220}{\frac{(Y+120)}{1000} + 0.220}$ ⚹ ∻Key Concept∻ ⚹ Molarity of a mixed solution ⚹ ∻Explanation∻ ⚹ The molarity of a mixed solution is calculated by dividing the total moles of solute by the total volume of the solution. ⚹◊What is the formula for calculating the new concentration of a solution when mixing two solutions of different concentrations?⍭ Generate me a similar question◊

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