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Step-by-Step Solution
Step 1: Identify the given data
• Volume of first solution, $V_1 = 480 \text{ mL}$
• Molarity of first solution, $M_1 = 1.5 \text{ M}$
• Volume of second solution, $V_2 = 520 \text{ mL}$
• Molarity of second solution, $M_2 = 1.2 \text{ M}$
Step 2: Write the formula for the resultant molarity
To find the molarity of the final mixture, use the formula:
$$
M_{\text{mixture}} = \frac{M_1 \times V_1 + M_2 \times V_2}{V_1 + V_2}.
$$
Step 3: Substitute the known values
Substitute $M_1, V_1, M_2,$ and $V_2$ into the formula:
$$
M_{\text{mixture}}
= \frac{(1.5) \times (480) + (1.2) \times (520)}{480 + 520}.
$$
Step 4: Calculate numerator and denominator
Numerator = $1.5 \times 480 + 1.2 \times 520 = 720 + 624 = 1344.$
Denominator = $480 + 520 = 1000.$
Step 5: Determine the final molarity
$$
M_{\text{mixture}} = \frac{1344}{1000} = 1.344 \text{ M}.
$$
Hence, the molarity of the final mixture is $1.344 \text{ M}$.
Additional Insight: Shortcut Check
Since $1.2 \text{ M}$ and $1.5 \text{ M}$ are mixed, the final molarity must be between these two values. Observing the options, $1.344 \text{ M}$ is the only value fitting in that range, providing a quick check.
