Question

When zinc is refined by electrolysis, the desired half reaction at the cathode is:

${\mathbf{\text{Zn}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{(aq) + 2e}}}^{\mathbf{\text{-}}}\mathbf{\to }\mathbf{\text{Zn(s)}}$

A competing reaction, which lowers the yield, is the formation of hydrogen gas:

${\mathbf{\text{2H}}}^{\mathbf{\text{+}}}{\mathbf{\text{(aq) + 2e}}}^{\mathbf{\text{-}}}\mathbf{\to }{\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

If $\mathbf{\text{91.50\%}}$of the current flowing results in zinc being deposited, while$\mathbf{\text{8.50\%}}$ produces hydrogen gas, how many litres of${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$ , measured at STP, form per kilogram of zinc?

Short answer

The amount oflitres of ${\text{H}}_{\text{2}}$, measured at STP, form per kilogram of zinc is obtained as: $31.83L/Kg$.

Step-by-step solution

Define chemical reaction

Chemical synthesis or, alternatively, chemical breakdown into two or more separate chemicals occurs when one component interacts with another to generate new material. These processes are known as chemical reactions, and they are generally irreversible until followed by other chemical reactions.

Step 2: How many litres of H2 , measured at STP, form per kilogram of zinc?

Assume that one kilogram of zinc is generated. Estimate the quantity in moles.

$\text{1,000gZn×}\frac{1mol}{65.38g}\text{=15.30molZn}$

Convert the moles of Zn to electrons and multiply by Faraday's constant to get the required charge. Two electrons are involved in the reaction${\text{Zn}}^{\text{2 +}}\to \text{Zn}$

$15.30mol\times \frac{2mo{l}^{-}}{molZn}\times \frac{\text{96500 C}}{{\text{1 mole}}^{\text{-}}}{\text{= 2.95×10}}^{\text{6}}\text{C}$

Multiply the charge for Zn by the current hydrogen-to-zinc ratio to get the charge needed to make ${\text{H}}_{\text{2}}$.

${\text{2.95×10}}^{\text{6}}\text{C×}\frac{\text{8.50}}{\text{91.50}}{\text{= 2.74×10}}^{\text{5}}\text{C}$

To get the moles of electron, divide the charge by Faraday's constant. Convert moles of electron to moles of ${\text{H}}_{\text{2}}$. The generation of hydrogen gas from two hydrogen ions requires two electrons.

${\text{2.74×10}}^{\text{5}}\text{C×}\frac{1mole-}{{\displaystyle \text{96500 C}}}\text{×}\frac{1molH}{2mo{l}^{-}}{\text{=1.42molH}}_{\text{2}}$

Using the conversion ratio $22.4L$/mol at STP, convert the moles of ${\text{H}}_{\text{2}}$kg to litres ( 1 atm, 273 K).

$1.42{\text{molH}}_{\text{2}}\text{×}\frac{22.4L}{mol}\text{= 31.83L}$

To get the L/Kg ratio, divide the volume by the kilogram of zinc originally utilized.

$\frac{{\displaystyle \text{31.83L}}}{1Kg}\text{= 31.83L/Kg}$

Therefore, the value is: $\text{31.83L/Kg}$.