Question

An unknown metal M is electrolyzed. It took 74.1 s for a current of 2.00 A to plate out 0.107 g of the metalfrom a solution containing M(NO₃)₃. Identify the metal.

Short answer

Theunknown metal is bismuth

Step-by-step solution

Given information

The mass of plate-out metal is 0.107 g. The time value is 74.1 s. The current can be given as 2 A. The reaction for Ru formation can be given as:$M^{3+}+3^{e-}\to M$

Mole number of electrons released

The number of moles of electron released with 2.5 A current and 50 mins can be expressed as:

$$\begin{gathered} Molesofelectron=\left(74.1s\right)\left(\frac{2C}{1s}\right)\left(\frac{1mol}{96485C}\right) \\ =0.00154mol \end{gathered}$$

The moles of Ruthenium produced in electrolysis can be expressed as follows:

$$\begin{gathered} Mole=\left(0.00154mol\right)\left(\frac{1mol}{3mol}\right) \\ =5.13\times {10}^{-4} \end{gathered}$$

Finding molar mass

The molar mass can be given as:

$$\begin{gathered} Molarmass=\frac{Givenmass}{moles} \\ =\frac{0.107g}{5.13\times {10}^{-4}mol} \\ Molarmass=208.6g/mol \end{gathered}$$

The metal with the above molar mass is bismuth.