Final answer:
The correctly balanced chemical equation for the reaction of lanthanum oxide with water is La2O3 + 3H2O → 2La(OH)3.
Step-by-step explanation:
To balance the chemical equation La2O3 + H2O → La(OH)3, we need to ensure that there are equal numbers of each type of atom on both sides of the equation. Looking at the options provided, the correct balance is option a. La2O3 + 3H2O → 2La(OH)3. We have two lanthanum (La) atoms on both sides, six oxygen (O) atoms (three from the water and three from the hydroxide), and six hydrogen (H) atoms (from the water and the hydroxide).