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Step 1:I'll solve this step by step using the precise LaTeX formatting guidelines you specified:
Step 2:: Understand the Conversion
A 5% solution means 5 grams per 100 mL of solution. We need to convert this to mg/mL.
Step 3:: Convert Percentage to Grams per 100 mL
5\% = \frac{5}{100} \times 100 \mathrm{~mL} = 5 \mathrm{~g}/100 \mathrm{~mL}
Step 4:: Convert Grams to Milligrams
5 \mathrm{~g} = 5 \times 10^{3} \mathrm{~mg}
Step 5:: Calculate mg per mL
\frac{5 \times 10^{3} \mathrm{~mg}}{100 \mathrm{~mL}} = 50 \mathrm{~mg}/\mathrm{mL}
Final Answer
The key steps were converting the percentage to grams, converting grams to milligrams, and then dividing by the volume to get mg/mL.
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