Sure, let's solve this problem step-by-step.
The balanced chemical equation given is:
[tex]\[ 2 H_2 + O_2 \rightarrow 2 H_2O \][/tex]
This equation tells us that 1 molecule of [tex]\( O_2 \)[/tex] (oxygen) produces 2 molecules of [tex]\( H_2O \)[/tex] (water).
Now, you are given [tex]\( 8.93 \times 10^{23} \)[/tex] molecules of [tex]\( O_2 \)[/tex] and you need to find out how many molecules of [tex]\( H_2O \)[/tex] are produced.
Step-by-step solution:
1. According to the balanced equation, 1 molecule of [tex]\( O_2 \)[/tex] results in 2 molecules of [tex]\( H_2O \)[/tex].
2. If you have [tex]\( 8.93 \times 10^{23} \)[/tex] molecules of [tex]\( O_2 \)[/tex], each molecule of [tex]\( O_2 \)[/tex] produces 2 molecules of [tex]\( H_2O \)[/tex].
So, to find the total number of [tex]\( H_2O \)[/tex] molecules:
[tex]\[ \text{Number of } H_2O \text{ molecules} = 2 \times (\text{Number of } O_2 \text{ molecules}) \][/tex]
[tex]\[ \text{Number of } H_2O \text{ molecules} = 2 \times 8.93 \times 10^{23} \][/tex]
[tex]\[ \text{Number of } H_2O \text{ molecules} = 1.786 \times 10^{24} \][/tex]
So, the number of [tex]\( H_2O \)[/tex] molecules produced is [tex]\( 1.786 \times 10^{24} \)[/tex].
But considering significant figures and usual rounding conventions in scientific calculations:
[tex]\[ 1.786 \times 10^{24} \text{ can be rounded to } 1.79 \times 10^{24} \][/tex]
Therefore, the correct answer is:
[tex]\[ 1.79 \times 10^{24} \text{ molecules of } H_2O\][/tex]
So, the correct choice among the given options is:
[tex]\[ \boxed{1.79 \times 10^{24} \text{ molecules } H_2O } \][/tex]
