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Chapter 18: Problem 83

Atomic masses can be determined by electrolysis. In one hour, a current of \(0.600\) A deposits \(2.42 \mathrm{~g}\) of a certain metal, \(\mathrm{M}\), which is present in solution as \(\mathrm{M}^{+}\) ions. What is the atomic mass of the metal?

Short Answer

Expert verified
Answer: The atomic mass of the metal is approximately 108 g/mol.

Step by step solution

01

Determine the electric charge passed

The first step is to calculate the total electric charge passed during electrolysis. Electric charge (Q) can be calculated using the formula: $$Q = It$$ where \(I\) is the current and \(t\) is the time (in seconds). The given current, \(I\), is 0.600 A and the time, \(t\), is 1 hour (which is equivalent to 3600 seconds). To find the charge, we just need to multiply these values: $$Q = (0.600 A)(3600 s) = 2160 C$$
02

Calculate the moles of the metal ions deposited

The second step is to calculate the moles of metal ions deposited during the electrolysis process. We will use Faraday's law of electrolysis to determine this: $$\text{moles of ions} = \frac{\text{charge}}{\text{Faraday's constant} \times \text{number of electrons per ion}}$$ We are given that the metal's ions have a charge of +1 (as \(\mathrm{M}^{+}\) ions), so the number of electrons per ion would also be 1. Faraday's constant is approximately \(9.65 \times 10^{4} \mathrm{C/mol}\). Now we can calculate the moles of ions deposited: $$\text{moles of ions} = \frac{2160 C}{(9.65 \times 10^{4} \mathrm{C/mol}) \times 1} \approx 0.0224 \mathrm{moles}$$
03

Calculate the atomic mass of the metal

Finally, we will determine the atomic mass of the metal using the relationship between moles, mass, and atomic mass: $$\text{atomic mass} = \frac{\text{mass}}{\text{moles}}$$ We are given that the mass of the metal deposited is 2.42 g. Now we can find the atomic mass of the metal: $$\text{atomic mass} = \frac{2.42 g}{0.0224 \mathrm{moles}} \approx 108 \mathrm{g/mol}$$ So the atomic mass of the metal is approximately 108 g/mol.

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Most popular questions from this chapter

In biological systems, acetate ion is converted to ethyl alcohol in a two- step process: \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+3 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{CHO}(a q)+\mathrm{H}_{2} \mathrm{O}\) \(E^{o \prime}=-0.581 \mathrm{~V}\) \(\mathrm{CH}_{3} \mathrm{CHO}(a q)+2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \quad E^{o \prime}=-0.197 \mathrm{~V}\) \(\left(E^{\circ \prime}\right.\) is the standard reduction voltage at \(25^{\circ} \mathrm{C}\) and \(\mathrm{pH}\) of \(7.00 .\) ) (a) Calculate \(\Delta G^{\circ \prime}\) for each step and for the overall conversion. (b) Calculate \(E^{\circ \prime}\) for the overall conversion.

Draw a diagram for a salt bridge cell for each of the following reactions. Label the anode and cathode, and indicate the direction of current flow throughout the circuit. (a) \(\mathrm{Zn}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cd}(s)\) (b) \(2 \mathrm{AuCl}_{4}^{-}(a q)+3 \mathrm{Cu}(s) \longrightarrow 2 \mathrm{Au}(s)+8 \mathrm{Cl}^{-}(a q)+3 \mathrm{Cu}^{2+}(a q)\) (c) \(\mathrm{Fe}(s)+\mathrm{Cu}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{Cu}(s)+\mathrm{Fe}(\mathrm{OH})_{2}(s)\)

Which of the following species will react with \(1 \mathrm{M} \mathrm{HNO}_{3}\) ? (a) \(\mathrm{I}^{-}\) (b) Fe (c) \(\mathrm{Ag}\) (d) \(\mathrm{Pb}\)

Write a balanced chemical equation for the overall cell reaction represented as (a) \(\mathrm{Ag}\left|\mathrm{Ag}^{+} \| \mathrm{Sn}^{4+}, \mathrm{Sn}^{2+}\right| \mathrm{Pt}\) (b) \(\mathrm{Al}\left|\mathrm{Al}^{3+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) (c) \(\mathrm{Pt}\left|\mathrm{Fe}^{2+}, \mathrm{Fe}^{3+} \| \mathrm{MnO}_{4}^{-}, \mathrm{Mn}^{2+}\right| \mathrm{Pt}\)

An electrolytic cell produces aluminum from \(\mathrm{Al}_{2} \mathrm{O}_{3}\) at the rate of ten kilograms a day. Assuming a yield of \(100 \%\), (a) how many moles of electrons must pass through the cell in one day? (b) how many amperes are passing through the cell? (c) how many moles of oxygen \(\left(\mathrm{O}_{2}\right)\) are being produced simultaneously?
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