The compound sucrose is commonly known as table sugar. The chemical formula of sucrose is C12H22011-
How many hydrogen atoms are present in 55.7 mg of sucrose? (Avogadro’s number is N_{0} = 6.022e + 23 )
a) There are 4.05e + 21 hydrogen atoms present.
b) There are 2.16e + 27 hydrogen atoms present.
c) There are 4.45e + 18 hydrogen atoms present.
d) There are 2.16e + 21 hydrogen atoms present.
e) There are 2.16e + 24 hydrogen atoms present.
The Correct Answer and Explanation is :
To solve the problem, we need to determine how many hydrogen atoms are present in 55.7 mg of sucrose (C₁₂H₂₂O₁₁).
Step 1: Determine the molar mass of sucrose.
The molar mass of sucrose is the sum of the atomic masses of all atoms in its formula:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
- Oxygen (O): 16.00 g/mol
The molar mass of sucrose, C₁₂H₂₂O₁₁, is calculated as:
[
(12 \times 12.01) + (22 \times 1.008) + (11 \times 16.00) = 144.12 + 22.176 + 176.00 = 342.30 \, \text{g/mol}
]
Step 2: Calculate the moles of sucrose in 55.7 mg.
We need to convert the mass of sucrose from milligrams to grams and then calculate the number of moles:
[
55.7 \, \text{mg} = 0.0557 \, \text{g}
]
Now, calculate the number of moles:
[
\text{moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass}} = \frac{0.0557}{342.30} = 1.63 \times 10^{-4} \, \text{mol}
]
Step 3: Determine the number of hydrogen atoms in the sucrose sample.
From the chemical formula C₁₂H₂₂O₁₁, we see that there are 22 hydrogen atoms in one molecule of sucrose. Using Avogadro’s number (N₀ = 6.022 × 10²³ molecules/mol), we can calculate the number of molecules in 1.63 × 10⁻⁴ moles of sucrose:
[
\text{Number of molecules} = 1.63 \times 10^{-4} \, \text{mol} \times 6.022 \times 10^{23} = 9.83 \times 10^{19} \, \text{molecules}
]
Since each molecule contains 22 hydrogen atoms, the total number of hydrogen atoms is:
[
\text{Number of hydrogen atoms} = 9.83 \times 10^{19} \times 22 = 2.16 \times 10^{21} \, \text{hydrogen atoms}
]
Step 4: Conclusion
The correct answer is:
d) There are 2.16 × 10²¹ hydrogen atoms present.
Now, I’ll generate a diagram to illustrate this process.
Here’s a detailed illustration of the process for calculating the number of hydrogen atoms in sucrose, which includes the necessary steps and formulas. I hope it helps visualize the solution!
