Sure, let's break this down step-by-step to find the number of molecules present in 1296 grams of dinitrogen pentoxide (N\(_2\)O\(_5\)).
### Step 1: Understand the data provided
- Mass of dinitrogen pentoxide (N\(_2\)O\(_5\)): 1296 grams
- Molar mass of dinitrogen pentoxide: 108 grams per mole (g/mol)
- Avogadro's number: \( 6.022 \times 10^{23} \) molecules per mole (molecules/mol)
### Step 2: Calculate the number of moles
First, we need to find out how many moles of N\(_2\)O\(_5\) are in 1296 grams. This can be done using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{Number of moles} = \frac{1296 \text{ g}}{108 \text{ g/mol}} = 12 \text{ moles}
\][/tex]
### Step 3: Calculate the number of molecules
Now that we have the number of moles, we can use Avogadro's number to find the number of molecules. The formula to find the number of molecules is:
[tex]\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Using the numbers:
[tex]\[
\text{Number of molecules} = 12 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole}
\][/tex]
This gives:
[tex]\[
\text{Number of molecules} = 7.2264 \times 10^{24} \text{ molecules}
\][/tex]
### Step 4: Look at the provided answer choices
Given choices are:
A. \(1.199 \times 10^{24}\)
B. \(7.2269 \times 10^{25}\)
C. \(7.2269 \times 10^{24}\)
D. \(1.199 \times 10^{23}\)
E. \(7.2269 \times 10^{23}\)
Our calculated value is \(7.2264 \times 10^{24}\) molecules, which closely matches choice C.
### Conclusion
The correct answer is:
C. [tex]\(7.2269 \times 10^{24}\)[/tex]
