Calculate The Number Of Carbon Atoms In A 90.0 G Sample Of Glucose \left( C_6H_{12}O_6 \right ]. Be Sure Your Answer Has A Unit Symbol If Necessary, And Round It To 3 Significant Digits.

Mar 7, 2025 by ADMIN 187 views

**Calculating the Number of Carbon Atoms in a Sample of Glucose**

Introduction

Glucose, a simple sugar, is a vital source of energy for living organisms. It is composed of carbon, hydrogen, and oxygen atoms, with the molecular formula $\left( C_6H_{12}O_6 \right)$ . In this article, we will calculate the number of carbon atoms in a 90.0 g sample of glucose, rounding our answer to 3 significant digits.

Understanding the Molecular Formula

The molecular formula of glucose, $\left( C_6H_{12}O_6 \right)$ , indicates that one molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. To calculate the number of carbon atoms in a sample of glucose, we need to determine the molar mass of glucose and the number of moles of glucose present in the sample.

Calculating the Molar Mass of Glucose

The molar mass of glucose can be calculated by summing the atomic masses of its constituent atoms. The atomic masses of carbon, hydrogen, and oxygen are 12.01 g/mol, 1.008 g/mol, and 16.00 g/mol, respectively.

molar_mass_glucose = (6 * 12.01) + (12 * 1.008) + (6 * 16.00)
molar_mass_glucose = 180.16 g/mol

Calculating the Number of Moles of Glucose

To calculate the number of moles of glucose present in the sample, we can use the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the sample, and $M$ is the molar mass of glucose.

mass_sample = 90.0 g
moles_glucose = mass_sample / molar_mass_glucose
moles_glucose = 0.5 mol

Calculating the Number of Carbon Atoms

Now that we have the number of moles of glucose, we can calculate the number of carbon atoms present in the sample. Since each molecule of glucose contains 6 carbon atoms, we can multiply the number of moles of glucose by Avogadro's number (6.022 x 10^23 molecules/mol) and then multiply by 6 to get the total number of carbon atoms.

avogadros_number = 6.022 x 10^23 molecules/mol
carbon_atoms = moles_glucose * avogadros_number * 6
carbon_atoms = 1.81 x 10^24 atoms

Conclusion

In this article, we calculated the number of carbon atoms in a 90.0 g sample of glucose, rounding our answer to 3 significant digits. We first determined the molar mass of glucose and then calculated the number of moles of glucose present in the sample. Finally, we used Avogadro's number to calculate the total number of carbon atoms present in the sample.

References

IUPAC, Compendium of Chemical Terminology, 2nd ed. (1997).
CRC Handbook of Chemistry and Physics, 97th ed. (2016).

Additional Resources

Glucose
Molar Mass
Avogadro's Number
Calculating the Number of Carbon Atoms in a Sample of Glucose: Q&A ====================================================================

Introduction

In our previous article, we calculated the number of carbon atoms in a 90.0 g sample of glucose, rounding our answer to 3 significant digits. In this article, we will address some common questions related to the calculation and provide additional information to help you better understand the process.

Q: What is the molecular formula of glucose?

A: The molecular formula of glucose is $\left( C_6H_{12}O_6 \right)$ , indicating that one molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms.

Q: How do I calculate the molar mass of glucose?

A: To calculate the molar mass of glucose, you need to sum the atomic masses of its constituent atoms. The atomic masses of carbon, hydrogen, and oxygen are 12.01 g/mol, 1.008 g/mol, and 16.00 g/mol, respectively.

molar_mass_glucose = (6 * 12.01) + (12 * 1.008) + (6 * 16.00)
molar_mass_glucose = 180.16 g/mol

Q: How do I calculate the number of moles of glucose present in the sample?

A: To calculate the number of moles of glucose present in the sample, you can use the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the sample, and $M$ is the molar mass of glucose.

mass_sample = 90.0 g
moles_glucose = mass_sample / molar_mass_glucose
moles_glucose = 0.5 mol

Q: How do I calculate the number of carbon atoms present in the sample?

A: To calculate the number of carbon atoms present in the sample, you can multiply the number of moles of glucose by Avogadro's number (6.022 x 10^23 molecules/mol) and then multiply by 6 to get the total number of carbon atoms.

avogadros_number = 6.022 x 10^23 molecules/mol
carbon_atoms = moles_glucose * avogadros_number * 6
carbon_atoms = 1.81 x 10^24 atoms

Q: What is the significance of rounding the answer to 3 significant digits?

A: Rounding the answer to 3 significant digits is a way to express the answer in a more concise and meaningful way. It also helps to reduce the impact of rounding errors and makes the answer easier to understand.

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

A: Yes, you can use this method to calculate the number of carbon atoms in other substances as long as you know the molecular formula and the molar mass of the substance.

Conclusion

In this article, we addressed some common questions related to calculating the number of carbon atoms in a sample of glucose. We provided additional information and examples to help you better understand the process and apply it to other substances.

References

IUPAC, Compendium of Chemical Terminology, 2nd ed. (1997).
CRC Handbook of Chemistry and Physics, 97th ed. (2016).