Question

What mass of barium is produced when molten BaCl2 is electrolyzed by a current $\mathbf{2}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}$A for $\mathbf{6}\mathbf{.}\mathbf{00}\mathbf{}\mathit{h}$?

Short answer

The Mass of barium$3.85\times {10}^{3}kg$

Step-by-step solution

Definition of mass of barium

Barium has an atomic mass of $\text{137.327u}$. The mass of an atom is defined as its atomic mass. The atomic mass, also known as relative isotopic mass, refers to the mass of a single particle and is thus associated with a specific isotope of an element.

Find mass of barium

Electrical current is electrical charge transferred in a particular time.These three properties can be calculated using the equation shown below.

$\text{I =}\frac{\text{q}}{\text{t}}$

We can use the equation shown above for calculating the charge transferred in a particular time.

$$\begin{gathered} q=I\times t=2.50\times A\times 21,600s \\ q=5.40\times {10}^{9}C \end{gathered}$$

Find the mole of an electron with the mole of barium

Next, we can relate the moles of electrons with the moles of barium.If you look at the figure below, you can see that the mole ratio is 1 to 2.
$$\begin{gathered} n\left(Ba\right)=0.5\times n\left(e^{-}\right)=0.5\times 5.6\times {10}^{4}mol \\ n\left(Ba\right)=2.8\times {10}^{4}mol \end{gathered}$$

$$\begin{gathered} {\text{BaCl}}_{\text{2}}\text{(s)}\to \stackrel{∆}{n}B{a}^{2+}+2C{l}^{-} \\ {\text{Cathode:Ba}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}\to \text{nBa} \\ {\text{Anode:2Cl}}^{\text{-}}\to {\text{nCl}}_{\text{2}}{\text{+ 2e}}^{\text{-}} \\ {\text{Ba}}^{\text{2 +}}{\text{+ 2Cl}}^{\text{-}}\to {\text{nBa + Cl}}_{\text{2}} \end{gathered}$$

Find mass of barium

mass (Ba) = n(Ba) Molar mass (Ba)

mass (Ba) = $2.8\times {10}^{4}mol\times 137.33g/mol$

$$\begin{gathered} 3.85\times {10}^{6}g=3.85\times {10}^{3}kg \\ mass\left(Ba\right)=3.85\times {10}^{3}kg \end{gathered}$$

Then the mass of barium is s