How Many Oxygen Atoms Are There In 5.00 G Of Sodium Dichromate, $Na_2Cr_2O_7$?A. $8.04 \times 10^{22}$ Oxygen AtomsB. $0.133$ Oxygen AtomsC. $1.64 \times 10^{21}$ Oxygen AtomsD. $1.15 \times 10^2$ Oxygen Atoms

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Introduction

Sodium dichromate, Na2Cr2O7Na_2Cr_2O_7, is a chemical compound that consists of sodium, chromium, and oxygen atoms. In this article, we will calculate the number of oxygen atoms present in 5.00 g of sodium dichromate. To do this, we will use the molar mass of sodium dichromate and the Avogadro's number to find the number of oxygen atoms.

Molar Mass of Sodium Dichromate

The molar mass of sodium dichromate is the sum of the atomic masses of its constituent elements. The atomic masses of sodium (Na), chromium (Cr), and oxygen (O) are 22.99 g/mol, 51.996 g/mol, and 16.00 g/mol, respectively. Therefore, the molar mass of sodium dichromate is:

MNa2Cr2O7=2(22.99)+2(51.996)+7(16.00)M_{Na_2Cr_2O_7} = 2(22.99) + 2(51.996) + 7(16.00)

MNa2Cr2O7=45.98+103.992+112.00M_{Na_2Cr_2O_7} = 45.98 + 103.992 + 112.00

MNa2Cr2O7=261.972 g/molM_{Na_2Cr_2O_7} = 261.972 \text{ g/mol}

Number of Moles of Sodium Dichromate

To find the number of moles of sodium dichromate, we will divide the given mass (5.00 g) by the molar mass (261.972 g/mol):

nNa2Cr2O7=mNa2Cr2O7MNa2Cr2O7n_{Na_2Cr_2O_7} = \frac{m_{Na_2Cr_2O_7}}{M_{Na_2Cr_2O_7}}

nNa2Cr2O7=5.00 g261.972 g/moln_{Na_2Cr_2O_7} = \frac{5.00 \text{ g}}{261.972 \text{ g/mol}}

nNa2Cr2O7=0.0191 moln_{Na_2Cr_2O_7} = 0.0191 \text{ mol}

Number of Oxygen Atoms

To find the number of oxygen atoms, we will use the Avogadro's number (6.022 x 10^23 atoms/mol) and the number of moles of sodium dichromate:

NO=nNa2Cr2O7×NAN_{O} = n_{Na_2Cr_2O_7} \times N_A

NO=0.0191 mol×6.022×1023 atoms/molN_{O} = 0.0191 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol}

NO=1.145×1022 atomsN_{O} = 1.145 \times 10^{22} \text{ atoms}

However, we need to consider that there are 7 oxygen atoms in each molecule of sodium dichromate. Therefore, the total number of oxygen atoms is:

NO=7×1.145×1022 atomsN_{O} = 7 \times 1.145 \times 10^{22} \text{ atoms}

NO=8.035×1022 atomsN_{O} = 8.035 \times 10^{22} \text{ atoms}

Conclusion

In conclusion, there are approximately 8.04 x 10^22 oxygen atoms in 5.00 g of sodium dichromate. This is the correct answer among the given options.

References

  • CRC Handbook of Chemistry and Physics, 97th Edition
  • IUPAC, Compendium of Chemical Terminology, 2nd Edition

Discussion

This problem requires the use of the molar mass of sodium dichromate and the Avogadro's number to find the number of oxygen atoms. The molar mass is calculated by summing the atomic masses of its constituent elements, and the Avogadro's number is used to convert the number of moles to the number of atoms. The total number of oxygen atoms is then calculated by multiplying the number of moles by the Avogadro's number and considering the number of oxygen atoms in each molecule of sodium dichromate.

Limitations

This problem assumes that the given mass of sodium dichromate is pure and free of impurities. In reality, the actual number of oxygen atoms may be different due to the presence of impurities or other factors. Additionally, this problem uses the molar mass of sodium dichromate, which may not be exact due to the uncertainty in the atomic masses of its constituent elements.

Future Work

This problem can be extended to calculate the number of oxygen atoms in other compounds that contain oxygen. Additionally, the effect of impurities or other factors on the actual number of oxygen atoms can be investigated.

Q: What is the molar mass of sodium dichromate?

A: The molar mass of sodium dichromate is 261.972 g/mol, which is calculated by summing the atomic masses of its constituent elements: sodium (Na), chromium (Cr), and oxygen (O).

Q: How do I calculate the number of moles of sodium dichromate?

A: To calculate the number of moles of sodium dichromate, you need to divide the given mass (in grams) by the molar mass (in g/mol). For example, if you have 5.00 g of sodium dichromate, the number of moles would be:

nNa2Cr2O7=mNa2Cr2O7MNa2Cr2O7n_{Na_2Cr_2O_7} = \frac{m_{Na_2Cr_2O_7}}{M_{Na_2Cr_2O_7}}

nNa2Cr2O7=5.00 g261.972 g/moln_{Na_2Cr_2O_7} = \frac{5.00 \text{ g}}{261.972 \text{ g/mol}}

nNa2Cr2O7=0.0191 moln_{Na_2Cr_2O_7} = 0.0191 \text{ mol}

Q: How do I calculate the number of oxygen atoms in sodium dichromate?

A: To calculate the number of oxygen atoms in sodium dichromate, you need to use the Avogadro's number (6.022 x 10^23 atoms/mol) and the number of moles of sodium dichromate. For example, if you have 0.0191 mol of sodium dichromate, the number of oxygen atoms would be:

NO=nNa2Cr2O7×NAN_{O} = n_{Na_2Cr_2O_7} \times N_A

NO=0.0191 mol×6.022×1023 atoms/molN_{O} = 0.0191 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol}

NO=1.145×1022 atomsN_{O} = 1.145 \times 10^{22} \text{ atoms}

However, you need to consider that there are 7 oxygen atoms in each molecule of sodium dichromate. Therefore, the total number of oxygen atoms is:

NO=7×1.145×1022 atomsN_{O} = 7 \times 1.145 \times 10^{22} \text{ atoms}

NO=8.035×1022 atomsN_{O} = 8.035 \times 10^{22} \text{ atoms}

Q: What is the significance of Avogadro's number in calculating the number of oxygen atoms?

A: Avogadro's number (6.022 x 10^23 atoms/mol) is a fundamental constant in chemistry that relates the number of moles of a substance to the number of atoms or molecules. It is used to convert the number of moles to the number of atoms or molecules, and is essential in calculating the number of oxygen atoms in sodium dichromate.

Q: Can I use this method to calculate the number of oxygen atoms in other compounds that contain oxygen?

A: Yes, you can use this method to calculate the number of oxygen atoms in other compounds that contain oxygen. However, you need to know the molar mass of the compound and the number of oxygen atoms in each molecule.

Q: What are some common sources of error in calculating the number of oxygen atoms?

A: Some common sources of error in calculating the number of oxygen atoms include:

  • Impurities in the sample
  • Uncertainty in the molar mass of the compound
  • Incorrect calculation of the number of moles
  • Incorrect use of Avogadro's number

Q: How can I improve the accuracy of my calculations?

A: To improve the accuracy of your calculations, you can:

  • Use high-purity samples
  • Use accurate values for the molar mass of the compound
  • Double-check your calculations for errors
  • Use a calculator or computer program to perform calculations

Q: What are some real-world applications of calculating the number of oxygen atoms?

A: Calculating the number of oxygen atoms has many real-world applications, including:

  • Chemistry and chemical engineering
  • Materials science and nanotechnology
  • Environmental science and pollution control
  • Biomedical research and medicine

Q: Can I use this method to calculate the number of oxygen atoms in other elements?

A: Yes, you can use this method to calculate the number of oxygen atoms in other elements that contain oxygen. However, you need to know the molar mass of the element and the number of oxygen atoms in each molecule.

Q: What are some common misconceptions about calculating the number of oxygen atoms?

A: Some common misconceptions about calculating the number of oxygen atoms include:

  • Thinking that the number of oxygen atoms is always a whole number
  • Assuming that the molar mass of the compound is always accurate
  • Not considering the number of oxygen atoms in each molecule
  • Not using Avogadro's number correctly

Q: How can I learn more about calculating the number of oxygen atoms?

A: You can learn more about calculating the number of oxygen atoms by:

  • Reading chemistry textbooks and online resources
  • Taking chemistry courses or workshops
  • Practicing calculations with different compounds and elements
  • Joining online forums or discussion groups for chemistry enthusiasts.