Question

See the following chemical reaction: \[ \text{Cr}_2\text{O}_7^{2-} + \text{XH}^+ + \text{6Fe}^{2+} \rightarrow \text{YCr}^{3+} + \text{6Fe}^{3+} + \text{ZH}_2\text{O}. \] The sum of \(X\), \(Y\), and \(Z\) is _____.

Answer 1

Correct Answer: 23

1. Balancing the Reaction: To balance the given reaction in an acidic medium: \[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}. \] 2. Identify \(X\), \(Y\), and \(Z\): - \(X = 14\) (moles of H\(^+\)), - \(Y = 2\) (moles of Cr\(^3+\)), - \(Z = 7\) (moles of H\(_2\)O). 3. Sum of \(X + Y + Z\): \[ X + Y + Z = 14 + 2 + 7 = 23. \] Final Answer: \( \boxed{23} \).