To measure the volume of an irregularly shaped container filled with water, 1.00 mL of 2.00 M potassium chloride solution is added. After stirring, a 5.00 mL sample was found to contain 2.54 × 10^-2 mg of potassium ion. What is the volume of the container?

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Quizplus · Accepted Answer

The concentration of the potassium chloride solution before dilution is:$$C_1 = 2.00 	ext{ M}$$The volume of the potassium chloride solution added is:$$V_1 = 1.00 	ext{ mL}$$The concentration of the potassium chloride solution after dilution is:$$C_2 = \frac{C_1V_1}{V_2}$$where V2 is the volume of the container.The mass of potassium ion in the 5.00 mL sample is:$$m = 2.54 	imes 10^{-2} 	ext{ mg}$$The moles of potassium ion in the 5.00 mL sample is:$$n = \frac{m}{M}$$where M is the molar mass of potassium ion (39.10 g/mol).The volume of the container is:$$V_2 = \frac{C_1V_1}{C_2}$$$$V_2 = \frac{(2.00 	ext{ M})(1.00 	ext{ mL})}{2.54 	imes 10^{-2} 	ext{ mg} / 5.00 	ext{ mL} 	imes 39.10 	ext{ g/mol}}$$$$V_2 = 15.4 	ext{ L}$$

To Measure the Volume of an Irregularly Shaped Container Filled