Question

Number of B - O bond in Peroxoborate is x and number of mole of $H_2(g)$ given by hydrolysis of 1 mole of $B_2H_6$ is y then find $\frac{x + y}{2}$

Answer 1

7

Answer 2

The question asks for the value of $\frac{x+y}{2}$, where x is the number of B-O bonds in Peroxoborate and y is the number of moles of $H_2(g)$ given by hydrolysis of 1 mole of $B_2H_6$.

Step 1: Determine the number of B-O bonds in Peroxoborate (x).

The most common peroxoborate salt is sodium peroxoborate tetrahydrate, $Na_2[B_2(O_2)_2(OH)_4] \cdot 6H_2O$. The anion is $[B_2(O_2)_2(OH)_4]^{2-}$.

In this dimeric anion, the structure consists of two boron atoms linked by two peroxo bridges ($O_2^{2-}$). Each boron atom is also bonded to two hydroxyl groups ($OH^-$).

Each boron atom is tetrahedrally coordinated to four oxygen atoms: two oxygen atoms from the two different peroxo bridges and two oxygen atoms from the two different hydroxyl groups.

So, each boron atom forms 4 B-O single bonds. Since there are two boron atoms in the anion, the total number of B-O bonds is $2 \times 4 = 8$.

Thus, $x = 8$.

Step 2: Determine the number of moles of $H_2(g)$ given by hydrolysis of 1 mole of $B_2H_6$ (y).

Diborane ($B_2H_6$) reacts with water (hydrolysis) to produce boric acid ($H_3BO_3$) and hydrogen gas ($H_2$). The balanced chemical equation for the hydrolysis of diborane is:

$B_2H_6(g) + 6H_2O(l) \rightarrow 2H_3BO_3(aq) + 6H_2(g)$

From the stoichiometry of the reaction, 1 mole of $B_2H_6$ reacts with excess water to produce 6 moles of $H_2(g)$.

Thus, $y = 6$.

Step 3: Calculate the value of $\frac{x+y}{2}$.

We have $x = 8$ and $y = 6$.

$\frac{x+y}{2} = \frac{8+6}{2} = \frac{14}{2} = 7$.