Question

Use the balanced equation to solve the problem.2H₂O → 2H₂ + O₂40.9L O₂ gas are made when water decomposes at STP.What mass of H₂O reacted?g

Answer 1

The mass of H2O that reacted is 65.88 grams

Step-by-step explanation

Given that;

The volume of oxygen atom at STP is 40.9L

Follow the steps below to find the mass of water reacted

Step 1; Write the balanced equation of the reaction

`\text{ 2H}_2O_((g))\text{ }\rightarrow\text{ 2H}_(2(g))\text{ + O}_(2(g))`

Step 2; Find the number of moles of oxygen atom

Recall, that 1 moles of a gas at STP is equivalent to 22.4 L/mol

Let x represents the number of moles of oxygen

`\begin{gathered} \text{ 1 mole O}_2\text{ }\rightarrow\text{ 22.4l/mol} \\ \text{ x mole O}_2\text{ }\rightarrow\text{ 40.9 L} \\ \text{ Cross multiply} \\ \text{ 1 mole O}_2\text{ }*\text{ 40.9L = x mole O}_2*\text{ 22.4 L/mol} \\ \text{ Isolate x mole O}_2 \\ \text{ x mole O}_2\text{ = }\frac{1\text{ mole O}_2*40.9\cancel{L}}{22.4\text{ }\frac{\cancel{L}}{mol}} \\ \\ \text{ x mole O}_2\text{ = }\frac{1\text{ }*\text{ 40.9}}{22.4} \\ \text{ x mole O}_2\text{ = }(40.9)/(22.4) \\ \text{ x mole O}_2\text{ = 1.83 moles} \end{gathered}`

The moles of O2 is 1.83 moles

Step 3; Find the number of moles of H2O using a stoichiometry ratio

Let x represents the number of moles of H2O

In the given reaction, 2 moles of water give 1 mole of O2

`\begin{gathered} \text{ 1 mole O}_2\text{ }\rightarrow\text{ 2 moles H}_2O \\ \text{ 1.83 moles O}_2\text{ }\rightarrow\text{ x moles H}_2O \\ \text{ cross multiply} \\ \text{ 1 mole O}_2\text{ }*\text{ x moles H}_2O\text{ = 2 moles H}_2O\text{ }*\text{ 1.83 moles O}_2 \\ \text{ Isolate x moles H}_2O\text{ } \\ \text{ x moles H}_2O\text{ = }\frac{\text{ 2 moles H}_2O*1.83moles\cancel{O_2}}{1mole\cancel{O_2}} \\ \\ \text{ x moles H}_2O\text{ = 2 }*\text{ 1.83} \\ \text{ x moles H}_2O\text{ = 3.66 moles} \end{gathered}`

The number of moles of H2O is 3.66 moles

Step 4; Find the mass of H2O using the formula below

`\begin{gathered} \text{ mole = }\frac{\text{ mass}}{\text{ molar mass}} \\ \text{ cross multiply} \\ \text{ mass = mole }*\text{ molar mass} \end{gathered}`

Recall, that the molar mass of water is 18.0 g/mol

`\begin{gathered} \text{ mass = 3.66 }*\text{ 18} \\ \text{ mass = 65.88 grams} \end{gathered}`

Therefore, the mass of H2O that reacted is 65.88 grams