Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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

Sagot :

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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.