200 microliters of a standard solution of 0.200 mg/mL caffeine was mixed with 4.8 mL of 50 mM sodium phosphate buffer, pH 3: methanol (60:40 v/v). What is the concentration of caffeine, in mg/mL, in this solution? Give your answer to two significant figures.

Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
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Chapter1: Biochemistry: An Evolving Science
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**Problem Statement:**

200 microliters of a standard solution of 0.200 mg/mL caffeine was mixed with 4.8 mL of 50 mM sodium phosphate buffer, pH 3: methanol (60:40 v/v). What is the concentration of caffeine, in mg/mL, in this solution? Give your answer to two significant figures.

**Solution:**

This problem requires the calculation of the concentration of caffeine in a mixed solution. Here is how to solve it step-by-step.

1. **Calculate the Total Volume of the Solution:**
   - Volume of caffeine solution = 200 microliters = 0.200 mL
   - Volume of buffer solution = 4.8 mL
   - Total volume = 0.200 mL + 4.8 mL = 5.0 mL

2. **Calculate the Amount of Caffeine:**
   - Concentration of caffeine solution = 0.200 mg/mL
   - Amount of caffeine = concentration × volume = 0.200 mg/mL × 0.200 mL = 0.040 mg

3. **Calculate the New Concentration of Caffeine in the Mixed Solution:**
   - New concentration = amount of caffeine / total volume
   - New concentration = 0.040 mg / 5.0 mL = 0.0080 mg/mL

Thus, the concentration of caffeine in the mixed solution is **0.0080 mg/mL** (to two significant figures).
Transcribed Image Text:**Problem Statement:** 200 microliters of a standard solution of 0.200 mg/mL caffeine was mixed with 4.8 mL of 50 mM sodium phosphate buffer, pH 3: methanol (60:40 v/v). What is the concentration of caffeine, in mg/mL, in this solution? Give your answer to two significant figures. **Solution:** This problem requires the calculation of the concentration of caffeine in a mixed solution. Here is how to solve it step-by-step. 1. **Calculate the Total Volume of the Solution:** - Volume of caffeine solution = 200 microliters = 0.200 mL - Volume of buffer solution = 4.8 mL - Total volume = 0.200 mL + 4.8 mL = 5.0 mL 2. **Calculate the Amount of Caffeine:** - Concentration of caffeine solution = 0.200 mg/mL - Amount of caffeine = concentration × volume = 0.200 mg/mL × 0.200 mL = 0.040 mg 3. **Calculate the New Concentration of Caffeine in the Mixed Solution:** - New concentration = amount of caffeine / total volume - New concentration = 0.040 mg / 5.0 mL = 0.0080 mg/mL Thus, the concentration of caffeine in the mixed solution is **0.0080 mg/mL** (to two significant figures).
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