Question

What mass of each of the following substances can be produced in 1.0 h with a current of 15 A?
a. Co from aqueous Co²⁺
b. Hf from aqueous Hf⁴⁺

c. I₂ from aqueous KI

d. Cr from molten CrO³

Short answer

Themass produced in 1.0 h with a current of 15 A of the following substances are as follows

(a) The mass of Co-produced is 16 g

(b) The mass of Hf produced is 25 g

(c) The mass of I₂ produced is 71 g

(d) The mass of Cr produced is 4.9 g

Step-by-step solution

Step 1(a): Mass of Co produced in 1 h

The reduction reaction can be denoted as,

${\mathrm{Co}}^{2+}+2{\mathrm{e}}^{-}\to \mathrm{Co}$

The mole number of electron can be denoted as,

$\begin{array}{rcl}\mathrm{Moles} \mathrm{of} \mathrm{electron}& =& (1 \mathrm{h})\left(\frac{60 \min }{1 \mathrm{hr}}\right)\left(\frac{60 \mathrm{s}}{1 \min }\right)\left(\frac{15 \mathrm{C}}{1 \mathrm{s}}\right)\left(\frac{1 \mathrm{mol}}{96485 \mathrm{C}}\right)\\ & =& 0.56 \mathrm{mol}\end{array}$

The mass of Co produced can be calculated as,

$\begin{array}{rcl}\mathrm{Mass}& =& (0.56 \mathrm{mol})\left(\frac{1 \mathrm{mol} \mathrm{Co}}{2 \mathrm{mol}}\right)\left(\frac{58.9 \mathrm{g} \mathrm{Co}}{1 \mathrm{mol} \mathrm{Co}}\right)\\ & =& 16 \mathrm{g}\end{array}$

Step 2(b): Mass of Hf produced in 1 h

The reduction reaction can be denoted as,

${\mathrm{Hf}}^{4+}+4{\mathrm{e}}^{-}\to \mathrm{Hf}$

The mole number of electron can be denoted as,

$\begin{array}{rcl}\mathrm{Moles} \mathrm{of} \mathrm{electron}& =& (1 \mathrm{h})\left(\frac{60 \min }{1 \mathrm{hr}}\right)\left(\frac{60 \mathrm{s}}{1 \min }\right)\left(\frac{15 \mathrm{C}}{1 \mathrm{s}}\right)\left(\frac{1 \mathrm{mol}}{96485 \mathrm{C}}\right)\\ & =& 0.56 \mathrm{mol}\end{array}$

The mass of Hf produced can be calculated as,

$\begin{array}{rcl}\mathrm{Mass}& =& (0.56 \mathrm{mol})\left(\frac{1 \mathrm{mol} \mathrm{Hf}}{2 \mathrm{mol}}\right)\left(\frac{178.5 \mathrm{g} \mathrm{Hf}}{1 \mathrm{mol} \mathrm{Hf}}\right)\\ & =& 25 \mathrm{g}\end{array}$

Step 3(c): Mass of I2 produced in 1 h

The reduction reaction can be denoted as,

$2{\mathrm{I}}^{-}+2{\mathrm{e}}^{-}\to {\mathrm{I}}_2$

The mole number of electron can be denoted as,

$\begin{array}{rcl}\mathrm{Moles} \mathrm{of} \mathrm{electron}& =& (1 \mathrm{h})\left(\frac{60 \min }{1 \mathrm{hr}}\right)\left(\frac{60 \mathrm{s}}{1 \min }\right)\left(\frac{15 \mathrm{C}}{1 \mathrm{s}}\right)\left(\frac{1 \mathrm{mol}}{96485 \mathrm{C}}\right)\\ & =& 0.56 \mathrm{mol}\end{array}$

The mass of I₂ produced can be calculated as,

$\begin{array}{rcl}\mathrm{Mass}& =& (0.56 \mathrm{mol})\left(\frac{1 \mathrm{mol} {\mathrm{I}}_2}{2 \mathrm{mol}}\right)\left(\frac{253.8 \mathrm{g} {\mathrm{I}}_2}{1 \mathrm{mol} {\mathrm{I}}_2}\right)\\ & =& 71 \mathrm{g}\end{array}$

Mass of Cr produced in 1 h                            

The reduction reaction can be denoted as,

${\mathrm{Cr}}^{6+}+6{\mathrm{e}}^{-}\to \mathrm{Cr}$

The mole number of electron can be denoted as,

$\begin{array}{rcl}\mathrm{Moles} \mathrm{of} \mathrm{electron}& =& (1 \mathrm{h})\left(\frac{60 \min }{1 \mathrm{hr}}\right)\left(\frac{60 \mathrm{s}}{1 \min }\right)\left(\frac{15 \mathrm{C}}{1 \mathrm{s}}\right)\left(\frac{1 \mathrm{mol}}{96485 \mathrm{C}}\right)\\ & =& 0.56 \mathrm{mol}\end{array}$

The mass of Cr produced can be calculated as,

$\begin{array}{rcl}\mathrm{Mass}& =& (0.56 \mathrm{mol})\left(\frac{1 \mathrm{mol} \mathrm{Cr}}{6 \mathrm{mol}}\right)\left(\frac{52 \mathrm{g} \mathrm{Cr}}{1 \mathrm{mol} \mathrm{Cr}}\right)\\ & =& 4.9 \mathrm{g}\end{array}$