How would you balance `"H"_3"BO"_3"``rarr``"H"_4"B"_6"O"_11" +H"_2"O"`?

This answer balances the equation by equating (the conservation of) the number of boron atoms on both sides of the equation.

`"H"_3"BO"_3` and `"H"_4"B"_6"O"_11` are the only two boron-containing species in this reaction. Each molecule of `"H"_3 color(navy)("B")"O"_3` contains one boron `"B"` atom whereas each molecule of `"H"_4color(navy)("B"_6)"O"_11` contains six. Add the coefficient `"color(navy)(6)` to the front of `"H"_3 "BO"_3` and `color(navy)(1)` to `"H"_4"B"_6"O"_11` balance the number of boron atoms on the two sides.

`color(purple)(6) color(white)(l)"H"_3color(navy)("B")"O"_3` `rarr` `color(purple)(1) color(white)(l) "H"_4color(navy)("B"_6) "O"_11 + "H"_2"O"` `color(grey)("NOT BALANCED")`

The left-hand side of the equation contains `6 xx 3 =18` oxygen `"O"` atoms. The number of oxygen atoms shall also conserve in this equation. Therefore `"H"_4"B"_6"O"_11` and `"H"_2"O"` on the product side shall contain a total of `18` oxygen atoms. `11` of them go to the `"H"_4color(navy)("B"_6)"O"_11` molecule. Water molecules would account for rest `7` oxygen atoms.

Each water molecule contains one single oxygen atom. `7` of the oxygen atoms would thus correspond to `7` water molecules on the product side. Hence the equation:

`color(black)(6) color(white)(l)"H"_3color(black)("B")"O"_3` `rarr` `color(black)(1) color(white)(l) "H"_4color(black)("B"_6) "O"_11 + color(purple)(7) color(white)(l) "H"_2"O"`

Optionally, check if the number of hydrogen `"H"` atoms on the two sides conserves to see if the equation is properly balanced:

• Number of `"H"` atoms on the right-hand side: `6 xx 3 = 18`
• Number of `"H"` atoms on the left-hand side: `1 xx 4 + 7 xx 2 = 18`

The two numbers are equal, and thus this chemical equation is stoichiometrically balanced.

`color(darkgreen)(6) color(white)(l)"H"_3color(black)("B")"O"_3` `rarr` `color(darkgreen)(1) color(white)(l) "H"_4color(black)("B"_6) "O"_11 + color(darkgreen)(7) color(white)(l) "H"_2"O"` `color(grey)("Balanced")`

Reference
"Balance Chemical Equation - Online Balancer," webqc.org,
https://www.webqc.org/balance.php, "Enter H3BO3 = H4B6O11 + H2O for this equation."