Math Problem Statement

How many grams in 5.033x10^24 atoms of Oxygen?

Solution

To find how many grams are in 5.033×10245.033 \times 10^{24} atoms of oxygen, we can follow these steps:

  1. Find the molar mass of oxygen:
    Oxygen has a molar mass of approximately 16 grams per mole (g/mol).

  2. Use Avogadro's number:
    Avogadro's number is 6.022×10236.022 \times 10^{23} atoms per mole. This tells us how many atoms are in 1 mole of oxygen.

  3. Convert atoms to moles:
    To convert the given number of atoms to moles, divide the number of atoms by Avogadro's number:
    Moles of oxygen=5.033×1024 atoms6.022×1023 atoms/mol\text{Moles of oxygen} = \frac{5.033 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}}

  4. Convert moles to grams:
    Once we know how many moles we have, we can multiply by the molar mass (16 g/mol) to find the mass in grams.

Let's calculate this:

Moles of oxygen=5.033×10246.022×10238.36 moles\text{Moles of oxygen} = \frac{5.033 \times 10^{24}}{6.022 \times 10^{23}} \approx 8.36 \text{ moles}

Now, multiply by the molar mass:

Mass of oxygen=8.36 moles×16 g/mol=133.76 grams\text{Mass of oxygen} = 8.36 \text{ moles} \times 16 \text{ g/mol} = 133.76 \text{ grams}

Thus, 5.033×10245.033 \times 10^{24} atoms of oxygen weigh approximately 133.76 grams.

Would you like more details or have any questions?

Here are 5 related questions for further understanding:

  1. How would the mass change for a different number of atoms?
  2. What is the role of Avogadro's number in these calculations?
  3. How do you convert from grams to atoms of a substance?
  4. Why is the molar mass of oxygen 16 g/mol?
  5. How does the concept of moles help in chemistry?

Tip: Always make sure to use the correct molar mass depending on the element's molecular form, like O2_2 for molecular oxygen.

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Math Problem Analysis

Mathematical Concepts

Stoichiometry
Molar Mass
Atoms to Moles Conversion

Formulas

Moles of oxygen = Atoms / Avogadro's number
Mass of oxygen = Moles of oxygen * Molar mass

Theorems

Avogadro's Number

Suitable Grade Level

Grades 10-12