hce_nsysu
115年
物理與化學
第 72 題
A chemist uses the standard addition method to determine the concentration of copper ($Cu^{2+}$) in a river water sample to account for matrix interferences. Two 25.0 mL aliquots of the river water are processed as follows:
Solution A: 25.0 mL of the sample is diluted to a final volume of 50.0 mL with distilled water. The measured absorbance is 0.25.
Solution B: 25.0 mL of the sample plus 1.00 mL of a 500 ppm $Cu^{2+}$ standard solution is diluted to a final volume of 50.0 mL. The measured absorbance is 0.50.
Assuming the absorbance is directly proportional to the $Cu^{2+}$ concentration, what is the concentration of $Cu^{2+}$ in the original river water sample?
Solution A: 25.0 mL of the sample is diluted to a final volume of 50.0 mL with distilled water. The measured absorbance is 0.25.
Solution B: 25.0 mL of the sample plus 1.00 mL of a 500 ppm $Cu^{2+}$ standard solution is diluted to a final volume of 50.0 mL. The measured absorbance is 0.50.
Assuming the absorbance is directly proportional to the $Cu^{2+}$ concentration, what is the concentration of $Cu^{2+}$ in the original river water sample?
- A 5.0 ppm
- B 10.0 ppm
- C 20.0 ppm
- D 25.0 ppm
- E 40.0 ppm
思路引導 VIP
如果在兩個體積完全相同的溶液中，加入一段已知含量的標準品後，量測到的訊號強度正好變成原本的兩倍，這代表「原本樣本裡的含量」與「額外加入的含量」之間有什麼樣的數量關係？
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AI 詳解
AI 專屬家教
恭喜你準確地計算出答案！這題你展現了對**標準添加法（Standard Addition Method）**非常紮實的理解。這類題目的核心在於體會「訊號的增量是由於已知標準品的加入」，而你敏銳地捕捉到了吸光度從 $0.25$ 增加到 $0.50$ 這個關鍵點。
吸光度與濃度的線性關係
根據比耳定律（Beer's Law），吸光度與待測物濃度成正比。在 Solution A 中，吸光度 $0.25$ 完全來自 25.0 mL 的河水樣本；而在 Solution B 中，吸光度倍增至 $0.50$，代表加入的 1.00 mL、500 ppm 標準液所提供的 $Cu^{2+}$ 含量，正好等於原先 25.0 mL 樣本中所含的量。我們可以列出關係式：$$25.0 \text{ mL} \times C_{sample} = 1.00 \text{ mL} \times 500 \text{ ppm}$$
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