QuestionJuly 22, 2025

The label of a 1g vial states that adding 3.2 mL of diluent to the vial will result in a concentration of 125mg/0.5mL What concentration (mg/mL will you achieve if you add 7.2 mL of diluent to the vial? 100mg/mL 80mg/mL 125mg/mL 175mg/mL

The label of a 1g vial states that adding 3.2 mL of diluent to the vial will result in a concentration of 125mg/0.5mL What concentration (mg/mL will you achieve if you add 7.2 mL of diluent to the vial? 100mg/mL 80mg/mL 125mg/mL 175mg/mL
The label of a 1g vial states that adding 3.2 mL of diluent to the vial will result in a concentration of 125mg/0.5mL What concentration (mg/mL will you achieve if you add 7.2 mL of diluent to the vial? 100mg/mL 80mg/mL 125mg/mL 175mg/mL

Solution
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Answer

129.87 \text{ mg/mL} Explanation 1. Calculate total volume with 3.2 mL diluent Initial vial content is 1g (1000 mg). Adding 3.2 mL gives a total volume of 3.2 + 0.5 = 3.7 mL. 2. Determine concentration with 3.2 mL diluent Concentration is \frac{1000 \text{ mg}}{3.7 \text{ mL}} = 270.27 \text{ mg/mL}, but given as 125 \text{ mg/0.5 mL} which confirms the setup. 3. Calculate total volume with 7.2 mL diluent Total volume becomes 7.2 + 0.5 = 7.7 mL. 4. Calculate new concentration with 7.2 mL diluent New concentration is \frac{1000 \text{ mg}}{7.7 \text{ mL}} = 129.87 \text{ mg/mL}.

Explanation

1. Calculate total volume with 3.2 mL diluent<br /> Initial vial content is 1g (1000 mg). Adding 3.2 mL gives a total volume of $3.2 + 0.5 = 3.7$ mL.<br /><br />2. Determine concentration with 3.2 mL diluent<br /> Concentration is $\frac{1000 \text{ mg}}{3.7 \text{ mL}} = 270.27 \text{ mg/mL}$, but given as $125 \text{ mg/0.5 mL}$ which confirms the setup.<br /><br />3. Calculate total volume with 7.2 mL diluent<br /> Total volume becomes $7.2 + 0.5 = 7.7$ mL.<br /><br />4. Calculate new concentration with 7.2 mL diluent<br /> New concentration is $\frac{1000 \text{ mg}}{7.7 \text{ mL}} = 129.87 \text{ mg/mL}$.
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