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Given an element having following ionisa...

Given an element having following ionisation enthalpies `IE_1 = 496 (kJ)/(mol)` and `IE_2 = 4562 (kJ)/(mol)` one mole hydroxide of this element is treated separated with `HCl` and `H_2SO_4` respectively. Moles of `HCl` and `H_2SO_4` reacted respectively is

A

1, `0.5`

B

`0.5`, 1

C

2, `0.5`

D

`0.5`, 2

Text Solution

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The correct Answer is:
To solve the problem, we need to determine how many moles of HCl and H2SO4 react with one mole of the hydroxide of the given element. We will analyze the ionization enthalpies provided and the reactions involved. ### Step 1: Analyze Ionization Enthalpies Given: - First Ionization Enthalpy (IE1) = 496 kJ/mol - Second Ionization Enthalpy (IE2) = 4562 kJ/mol The first ionization enthalpy is relatively low, indicating that it is easy to remove the first electron. The second ionization enthalpy is very high, suggesting that removing the second electron is much more difficult. This indicates that the element is likely a Group 1 metal (alkali metal), which typically has one valence electron. ### Step 2: Determine the Hydroxide Formula Since the element is a Group 1 metal, its hydroxide will be of the form \( MOH \), where \( M \) is the metal. For one mole of the hydroxide \( MOH \), we have: \[ \text{1 mole of } MOH \] ### Step 3: Reaction with HCl When the hydroxide reacts with hydrochloric acid (HCl), the reaction is as follows: \[ MOH + HCl \rightarrow MCl + H_2O \] From this reaction, we can see that 1 mole of \( MOH \) reacts with 1 mole of HCl. Therefore: \[ \text{Moles of HCl reacted} = 1 \text{ mole} \] ### Step 4: Reaction with H2SO4 When the hydroxide reacts with sulfuric acid (H2SO4), the reaction is: \[ 2 MOH + H_2SO_4 \rightarrow M_2SO_4 + 2 H_2O \] From this balanced equation, we see that 2 moles of \( MOH \) react with 1 mole of \( H_2SO_4 \). Therefore, for 1 mole of \( MOH \): \[ \text{Moles of } H_2SO_4 \text{ reacted} = \frac{1}{2} \text{ mole} = 0.5 \text{ mole} \] ### Final Answer Thus, the moles of HCl and H2SO4 that reacted with one mole of the hydroxide are: - Moles of HCl = 1 mole - Moles of H2SO4 = 0.5 mole ### Summary The final answer is: - Moles of HCl reacted = 1 - Moles of H2SO4 reacted = 0.5
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