QuestionBalance the equation $\mathrm{Ga}_{2} \mathrm{O}_{3}(s)+6 \mathrm{HCl}(aq) \rightarrow 2 \mathrm{GaCl}_{3}(aq)+3 \mathrm{H}_{2} \mathrm{O}(l)$ and perform stoichiometry calculations.

Studdy Solution

STEP 1

Assumptions1. The balanced chemical equation is $\mathrm{Ga}_{} \mathrm{}_{3}(s)+6 \mathrm{HCl}(a q) \rightarrow \mathrm{GaCl}_{3}(a q)+3 \mathrm{H}_{} \mathrm{}(l)$ . The equation is balanced, meaning the number of atoms of each element is the same on both sides of the equation3. Stoichiometry calculations will be based on the balanced equation

STEP 2

To understand the balancing of the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's start with the Gallium (Ga) atomsOn the left side, we have2 Ga atoms (from $\mathrm{Ga}_{2} \mathrm{}_{}$ ), and on the right side, we also have2 Ga atoms (from2 $\mathrm{GaCl}_{}$ ). So, the Ga atoms are balanced.
$\mathrm{Ga}_{2} \mathrm{}_{}(s)+6 \mathrm{HCl}(a q) \rightarrow2 \mathrm{GaCl}_{}(a q)+ \mathrm{H}_{2} \mathrm{}(l)$

STEP 3

Next, let's balance the Oxygen () atomsOn the left side, we have3 O atoms (from $\mathrm{Ga}_{2} \mathrm{}_{3}$ ), and on the right side, we have3 O atoms (from3 $\mathrm{H}_{2} \mathrm{}$ ). So, the O atoms are balanced.
$\mathrm{Ga}_{2} \mathrm{}_{3}(s)+6 \mathrm{HCl}(a q) \rightarrow2 \mathrm{GaCl}_{3}(a q)+3 \mathrm{H}_{2} \mathrm{}(l)$

STEP 4

Finally, let's balance the Hydrogen (H) and Chlorine (Cl) atomsOn the left side, we have6 H atoms and6 Cl atoms (from6 $\mathrm{HCl}$ ), and on the right side, we also have6 H atoms (from3 $\mathrm{H}_{2} \mathrm{}$ ) and6 Cl atoms (from2 $\mathrm{GaCl}_{3}$ ). So, the H and Cl atoms are balanced.
$\mathrm{Ga}_{2} \mathrm{}_{3}(s)+6 \mathrm{HCl}(a q) \rightarrow2 \mathrm{GaCl}_{3}(a q)+3 \mathrm{H}_{2} \mathrm{}(l)$

STEP 5

For stoichiometry calculations, we use the balanced equation to find the ratio of moles of reactants to products. From the balanced equation, we can see that1 mole of $\mathrm{Ga}_{2} \mathrm{}_{3}$ reacts with moles of $\mathrm{HCl}$ to produce2 moles of $\mathrm{GaCl}_{3}$ and3 moles of $\mathrm{H}_{2} \mathrm{}$ .
This ratio can be used to calculate the amount of reactants needed or products formed in a chemical reaction.

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