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Chapter 18: Problem 95

Electrolysis of an alkaline earth metal chloride using a current of 5.00 \(\mathrm{A}\) for 748 s deposits 0.471 \(\mathrm{g}\) of metal at the cathode. What is the identity of the alkaline earth metal chloride?

Short Answer

Expert verified
The identity of the alkaline earth metal chloride is magnesium chloride (MgCl₂).

Step by step solution

01

Calculate the total charge passed through the circuit

To calculate the total charge passed through the circuit, we can use the formula: Charge (Q) = Current (I) × Time (t) We are given the current (I) as 5.00 A and the time (t) as 748 s. So, we can substitute these values into the equation: Q = 5.00 A × 748 s = 3740 C (coulombs)
02

Calculate the number of Faradays used

Now, let's calculate the number of Faradays used in the electrolysis process. We know that one Faraday (F) of charge is equal to 96485 C/mol. Hence, we can find the number of Faradays by dividing the total charge (Q) by the charge of one Faraday (F): Number of Faradays = Q / F = 3740 C / 96485 C/mol ≈ 0.03875 mol
03

Calculate the amount of metal deposited per Faraday

We are given the mass of metal deposited on the cathode (0.471 g). To find the amount of metal deposited per Faraday, we can divide the mass of metal deposited by the number of Faradays used: Amount of metal deposited per Faraday = Mass of metal / Number of Faradays = 0.471 g / 0.03875 mol ≈ 12.15 g/mol
04

Determine the equivalent mass of the metal

The equivalent mass of the metal is the mass of the metal deposited per Faraday multiplied by the valence of the metal ion. Since the alkaline earth metals form ions with a +2 charge, the equivalent mass of the metal in this case will be twice the amount of the metal deposited per Faraday: Equivalent mass of metal = 2 × 12.15 g/mol ≈ 24.3 g/mol
05

Identify the alkaline earth metal based on its equivalent mass

We can now compare the equivalent mass we calculated with the molar masses of the alkaline earth metal to identify the metal. The alkaline earth metals and their molar masses are: - Beryllium (Be): 9.012 g/mol - Magnesium (Mg): 24.305 g/mol - Calcium (Ca): 40.078 g/mol - Strontium (Sr): 87.62 g/mol - Barium (Ba): 137.327 g/mol - Radium (Ra): 226 g/mol The equivalent mass we calculated, 24.3 g/mol, is closest to the molar mass of magnesium (Mg), which is 24.305 g/mol. Therefore, the identity of the alkaline earth metal chloride is magnesium chloride (MgCl₂).

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