How many electrons flow when a current of 5 A is passed through a solution for 200 s? — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Calculate the Total Electric Charge ($Q$) The relationship between electric current ($I$), time ($t$), and total electric charge ($Q$) is given by the formula: $$Q = I \times t$$ Given values in the problem: * Current, $I = 5\text{ A}$ * Time, $t = 200\text{ s}$ Substituting the given values into the formula: $$Q = 5\text{ A} \times 200\text{ s}$$ $$Q = 1000\text{ C}$$ Step 2 - Determine the Number of Electrons ($N$) The total charge ($Q$) is quantized and is an integral multiple of the elementary charge of a single electron ($e$): $$Q = N \times e$$ Where: * $N$ is the total number of electrons flowing through the solution. * $e$ is the charge of a single electron, which is approximately $1.602 \times 10^{-19}\text{ C}$. Rearranging the formula to solve for $N$: $$N = \frac{Q}{e}$$ Substituting the values: $$N = \frac{1000\text{ C}}{1.602 \times 10^{-19}\text{ C}}$$ $$N \approx 6.242 \times 10^{21}$$ Thus, the number of electrons flowing through the solution is approximately $\boxed{6.24 \times 10^{21}}$. Step 3 - Analysis of Options * **Option (A)** represents $6.022 \times 10^{23}$, which is Avogadro's number (the number of electrons in $1\text{ Faraday}$ of charge, i.e., $96500\text{ C}$). This is incorrect as our charge is only $1000\text{ C}$. * **Option (B)** represents $6.24 \times 10^{21}$, which matches our calculated value and is therefore the correct choice. * **Option (C)** represents $6.024 \times 10^{21}$, which is numerically incorrect. * **Option (D)** represents $6.022 \times 10^{20}$, which is off by a factor of ten and is incorrect. $$\text{Correct Option: } \boxed{\text{B}}$$