Answered

Passing an electric current through a sample of water [tex]$\left(H_2O\right)$[/tex] can cause the water to decompose into hydrogen gas [tex]$\left(H_2\right)$[/tex] and oxygen gas [tex]$\left(O_2\right)$[/tex] according to the following equation.

[tex]\[ 2H_2O \rightarrow 2H_2 + O_2 \][/tex]

The molar mass of [tex]$H_2O$[/tex] is [tex]$18.02 \, \text{g/mol}$[/tex]. The molar mass of [tex]$O_2$[/tex] is [tex]$32.00 \, \text{g/mol}$[/tex]. What mass of [tex]$H_2O$[/tex], in grams, must react to produce [tex]$50.00 \, \text{g}$[/tex] of [tex]$O_2$[/tex]?

A. 14.08 grams
B. 28.16 grams
C. 44.40 grams
D. 56.31 grams



Answer :

GinnyAnswer
First, recognize the chemical equation given for the decomposition of water:

[tex]\[ 2 H_2O \rightarrow 2 H_2 + O_2 \][/tex]

This balanced reaction shows that 2 moles of water (\(H_2O\)) produce 1 mole of oxygen gas (\(O_2\)).

Given:
- The mass of oxygen gas (\(O_2\)) produced is \(50.00\) grams.
- The molar mass of oxygen gas (\(O_2\)) is \(32.00\) grams per mole.
- The molar mass of water (\(H_2O\)) is \(18.02\) grams per mole.

### Step-by-Step Solution:

1. Calculate the moles of \( O_2 \) produced:

[tex]\[ \text{Moles of } O_2 = \frac{\text{Mass of } O_2}{\text{Molar mass of } O_2} \][/tex]

[tex]\[ \text{Moles of } O_2 = \frac{50.00 \text{ g}}{32.00 \text{ g/mol}} = 1.5625 \text{ moles} \][/tex]

2. Determine the moles of \( H_2O \) required using the stoichiometry of the reaction:

From the balanced equation, 2 moles of \( H_2O \) produce 1 mole of \( O_2 \).

Hence, to find the moles of \( H_2O \) required to produce \(1.5625\) moles of \( O_2 \):

[tex]\[ \text{Moles of } H_2O = 2 \times \text{Moles of } O_2 \][/tex]

[tex]\[ \text{Moles of } H_2O = 2 \times 1.5625 = 3.125 \text{ moles} \][/tex]

3. Calculate the mass of \( H_2O \) required:

[tex]\[ \text{Mass of } H_2O = \text{Moles of } H_2O \times \text{Molar mass of } H_2O \][/tex]

[tex]\[ \text{Mass of } H_2O = 3.125 \text{ moles} \times 18.02 \text{ g/mol} \][/tex]

[tex]\[ \text{Mass of } H_2O = 56.3125 \text{ grams} \][/tex]

Thus, the mass of \( H_2O \) that must react to produce \(50.00\) grams of \( O_2 \) is approximately \( 56.31 \) grams.

Therefore, the correct answer is:

[tex]\[ \boxed{56.31 \text{ grams}} \][/tex]